To accurately determine your face shape, measure the key dimensions of your face. Use a flexible measuring tape.
Measure across your cheekbones, just below the eyes.
Measure from the center of your hairline to the bottom of your chin.
Measure across the widest part of your forehead, usually mid-way between your eyebrows and hairline.
Measure from the point of your chin to the point just below your ear where the jaw angle turns upward. Multiply by 2 for the full jawline length.
Measure across the widest points of your cheekbones, usually just below the outer corner of your eyes.
Your Face Shape Analysis
Formula Used: This calculator analyzes ratios and comparisons between your facial measurements (width, height, forehead, jawline, cheekbones) to determine the most fitting geometric shape. It compares length to width, the prominence of cheekbones versus forehead, and the curvature or angularity of the jawline.
Comparison of Key Facial Measurements
Measurement
Your Value (Units)
Characteristic
Face Width
Face Height
Forehead Width
Cheekbone Width
Jawline Length
Summary of Your Facial Measurements
What is Face Shape Analysis?
Face shape analysis is the process of identifying the dominant geometric shape that best describes the overall structure of a person's face. It involves measuring key facial features like width, height, forehead, cheekbones, and jawline, and then comparing these measurements to identify patterns. Understanding your face shape is a fundamental concept in aesthetics, influencing decisions about hairstyles, eyewear, makeup application, and even clothing necklines. While there are general categories, most faces exhibit a combination of characteristics, making it more of an art than an exact science. This analysis is particularly popular in the beauty, fashion, and personal styling industries.
Who should use it? Anyone interested in personal styling, makeup artists, hairstylists, individuals looking to understand their features better, and those seeking to enhance their appearance by choosing flattering styles. It's also useful for understanding facial proportions for artistic purposes, such as portrait drawing or digital character creation.
Common misconceptions about face shape include believing there are only a few rigid categories, that one must perfectly fit a description, or that face shape is immutable. In reality, facial structures are complex and nuanced. Many people have oval-leaning-round faces or square-leaning-heart shapes. Furthermore, aging, weight fluctuations, and lifestyle can subtly alter facial contours over time. The goal is not to rigidly categorize but to understand the dominant lines and proportions to make informed styling choices.
Face Shape Formula and Mathematical Explanation
The face shape calculator employs a series of comparisons and ratio calculations derived from standard facial measurements. It's not a single, monolithic formula but a decision tree or weighted scoring system based on geometric principles. The primary goal is to determine which of the common face shapes (Oval, Round, Square, Oblong/Rectangle, Heart, Diamond) is the best fit.
Core Comparison Metrics:
Face Length vs. Face Width Ratio: This is a crucial starting point.
If Length ≈ Width: Suggests Round or Square.
If Length > Width: Suggests Oblong/Rectangle or Oval.
Cheekbone Width vs. Forehead Width:
If Cheekbones are Widest: Suggests Diamond or Heart.
If Forehead is Widest (or equal to cheekbones): Suggests Oval, Oblong, or Round.
If Jawline is Widest: Suggests Square or Round.
Jawline Shape:
Rounded Jaw: Points towards Round, Oval, or potentially Heart.
Angular/Sharp Jaw (often equal to or wider than forehead): Points towards Square or Oblong.
Derivation Logic (Simplified):
The calculator essentially applies a set of rules:
Oval: Face is longer than it is wide. Forehead is slightly wider than the jawline. Cheekbones are the widest part. Jawline is softly curved. (Length/Width Ratio > 1.3, Cheekbones >= Forehead, Jawline Rounded).
Round: Face length and width are nearly equal. Widest at the cheekbones. Jawline is rounded. (Length/Width Ratio ~ 1.0, Cheekbones Widest, Jawline Rounded).
Square: Face length and width are nearly equal. Forehead, cheekbones, and jawline are similar in width. Jawline is angular and strong. (Length/Width Ratio ~ 1.0, All widths similar, Jawline Angular).
Oblong/Rectangle: Face is longer than it is wide. Forehead, cheekbones, and jawline are similar in width. Jawline can be angular or slightly rounded. (Length/Width Ratio > 1.3, All widths similar).
Heart: Face is wider at the forehead and cheekbones, narrowing to a pointed or smaller chin. (Forehead Widest, Cheekbones slightly less, Jawline narrowest/pointed).
Diamond: Face is widest at the cheekbones. Forehead and jawline are narrower and roughly equal. Chin is pointed. (Cheekbones Widest, Forehead and Jawline narrower and similar, Chin pointed).
The calculator assigns points or checks conditions based on these comparisons to arrive at the most probable face shape.
Variables Used:
Variable
Meaning
Unit
Typical Range
Face Width (FW)
Horizontal measurement across the widest part of the face (usually cheekbones).
cm or inches
10.0 – 18.0 cm (4.0 – 7.0 in)
Face Height (FH)
Vertical measurement from hairline to chin.
cm or inches
15.0 – 25.0 cm (6.0 – 10.0 in)
Forehead Width (FHW)
Horizontal measurement across the widest part of the forehead.
cm or inches
10.0 – 17.0 cm (4.0 – 6.5 in)
Jawline Length (JL)
Measurement from chin to below the ear (x2).
cm or inches
15.0 – 22.0 cm (6.0 – 8.5 in)
Cheekbone Width (CBW)
Horizontal measurement across the widest points of the cheekbones.
cm or inches
10.0 – 18.0 cm (4.0 – 7.0 in)
Length/Width Ratio (LWR)
Ratio of Face Height to Face Width (FH / FW).
Ratio
0.7 – 1.7
Forehead Dominance Index (FDI)
Ratio comparing forehead width to face width (FHW / FW).
Ratio
0.6 – 1.0
Jawline Shape Indicator (JSI)
Comparison of jawline length relative to cheekbone width, or qualitative assessment.
Cheekbone Width vs. Face Width: 5.4 is slightly less than 5.5.
Forehead vs. Jawline: 5.3 (Forehead) > 4.0 (Jawline Length x 2 measurement implies chin point) – calculator logic interprets this as narrowing. More accurately, the jawline curve from ear to chin is relatively short compared to cheekbones, suggesting taper.
Jawline Shape: Rounded.
Calculator Output:
Primary Result: Oval
Length vs. Width Ratio: 1.36
Jawline Shape: Rounded/Tapered
Forehead Dominance: Forehead slightly wider than jawline, cheekbones near widest.
Interpretation: Sarah's face is longer than it is wide, with a gently tapering jawline and cheekbones being the widest point. This confirms an oval face shape. She can experiment with most hairstyles, including bangs, layers, and bobs, as they tend to balance her features.
Cheekbone Width vs. Face Width: 5.9 is very close to 6.0.
Forehead vs. Jawline: 5.8 (Forehead) is similar to 6.0 (Face Width implies jaw width). The full jawline length suggests a strong, defined angle.
Jawline Shape: Angular.
Calculator Output:
Primary Result: Square
Length vs. Width Ratio: 1.03
Jawline Shape: Angular
Forehead Dominance: Forehead, cheekbones, and jawline are similarly wide.
Interpretation: Mark's face is almost as long as it is wide, with a strong, angular jawline and roughly equal widths across his forehead, cheekbones, and jaw. This indicates a square face shape. Styles that soften the jawline, like layered haircuts, side parts, or styles with volume on top, can complement his features.
How to Use This Face Shape Calculator
Using our intuitive face shape calculator is straightforward. Follow these steps to get your results:
Gather Your Tools: You'll need a flexible measuring tape (like one used for sewing) and a mirror. Ensure good lighting.
Measure Your Face: Carefully measure the five key dimensions as described in the input fields:
Face Width: Widest part across cheekbones.
Face Height: From hairline center to chin bottom.
Forehead Width: Widest part of your forehead.
Cheekbone Width: Widest points of cheekbones.
Jawline Length: From chin point to below the ear (x2).
It's best to take each measurement at least twice to ensure accuracy. Record measurements in inches or centimeters, ensuring consistency.
Enter Measurements: Input your recorded measurements into the corresponding fields in the calculator. Avoid using currency symbols ($) as these are physical measurements.
Validate Inputs: The calculator will provide inline error messages if any input is missing, negative, or nonsensical (e.g., face width larger than height in an unrealistic way). Correct any errors before proceeding.
Calculate: Click the "Calculate My Face Shape" button.
Read Your Results:
Primary Result: This is the main face shape identified (e.g., Oval, Round, Square).
Intermediate Values: You'll see ratios and descriptions (e.g., Length vs. Width Ratio, Jawline Shape) that help explain the primary result.
Chart & Table: Review the bar chart and table for a visual and detailed breakdown of your measurements and their characteristics.
Understand the Formula: The "Formula Used" section provides a plain-language explanation of how the calculations are made.
Make Decisions: Use the insights gained to inform your choices regarding hairstyles, glasses frames, makeup techniques, or other styling preferences.
Reset: If you need to start over or try new measurements, click the "Reset" button to clear all fields and results.
Copy Results: Use the "Copy Results" button to easily share your findings or save them elsewhere.
Decision-Making Guidance: Remember that these are guidelines. The goal is to find styles that harmonize with your features and make you feel confident. If your measurements suggest a borderline shape (e.g., oval-square), consider the characteristics of both shapes.
Key Factors That Affect Face Shape Results
While the calculator relies on precise measurements, several underlying factors and considerations can influence the perception and accuracy of face shape analysis:
Measurement Accuracy: This is paramount. Even a slight error in measuring the widest point of the cheekbones versus the forehead can alter the calculated ratios. Factors like facial hair, makeup contouring, or not standing straight can skew results.
Facial Soft Tissue: Volume in the cheeks or fullness in the face due to body weight can make a face appear rounder or softer than its underlying bone structure suggests. Conversely, significant weight loss can emphasize bone structure, potentially making a face appear more angular.
Bone Structure Variations: Genetics dictates the underlying bone structure. Some people have naturally prominent cheekbones, a strong jaw, or a more delicate chin, which the measurements capture. However, subtle variations in bone growth or even past injuries can slightly alter proportions.
Hairline and Brow Shape: While not directly measured, the perceived shape of the forehead can be influenced by the hairline (widow's peak, receding hairline) and the shape of the eyebrows. A high hairline can make the forehead appear larger, potentially influencing the perception of a heart or oval shape.
Ageing Process: As people age, skin loses elasticity, fat distribution changes, and bone density can decrease. This can lead to a softening of angles, a less defined jawline, or a slight lengthening of the face, potentially shifting the perceived dominant face shape over time.
Facial Expressions and Muscle Tone: While static measurements are used, the way facial muscles are used and their resting tone can contribute to the overall appearance. A very strong masseter muscle can make the jawline appear wider and more square, for instance.
Asymmetry: Most faces are not perfectly symmetrical. The calculator typically uses the dominant side or an average. Significant asymmetry might mean the calculated shape is a generalization, and certain features might align better with a different shape.
Styling Choices (Hair, Makeup, Glasses): These are what face shape analysis aims to inform, but they can also retrospectively influence perception. Heavy contouring can create the illusion of a different jawline shape, or a specific hairstyle might emphasize or downplay certain features, making one face shape seem more prominent.
Frequently Asked Questions (FAQ)
Q: What units should I use for measurements?
A: You can use either inches or centimeters, as long as you are consistent across all measurements. The calculator works with ratios, so the unit itself doesn't matter, only that it's the same for all inputs.
Q: My measurements don't seem to fit any category perfectly. What does this mean?
A: It's very common! Most people have features that blend characteristics of multiple face shapes. The calculator identifies the *most dominant* shape based on the provided numbers. Consider yourself a blend, perhaps oval-square or round-heart, and choose styles that flatter the features you most want to emphasize or balance.
Q: Can my face shape change over time?
A: While your underlying bone structure remains the same, the *appearance* of your face shape can change due to factors like weight fluctuations, aging (loss of skin elasticity, fat redistribution), and even dental health. The calculator measures your current state.
Q: How do I measure my jawline accurately?
A: Locate the point just below your ear where your jaw angles upwards. Measure from that point to the tip of your chin. Then, do the same for the other side and add them together, OR simply measure one side and multiply by two if your jaw is relatively symmetrical. Ensure the tape follows the curve of your jaw.
Q: Should I measure with or without hair?
A: Measure the actual bone structure and facial contours. Pull your hair back completely away from your face (including sideburns) so that it doesn't interfere with your measurements, especially around the hairline and jaw.
Q: What if I have significant facial hair (beard/stubble)?
A: Facial hair can obscure the jawline and face width. For the most accurate results, try to measure the underlying structure as best as possible. You might need to feel for the bone structure beneath the hair. If it's impossible to get a clear measurement, the results might be less reliable.
Q: Are there other face shapes besides the main ones?
A: Yes, there are many nuanced variations and less common classifications (e.g., oblong-round, inverted triangle). The calculator focuses on the most widely recognized shapes for general styling purposes.
Q: How does face shape relate to beauty standards?
A: Historically, the oval shape has often been considered the most "balanced" or "ideal" in Western aesthetics because its proportions are thought to be harmonious. However, beauty is diverse, and every face shape has unique characteristics that can be considered beautiful and stylish when understood and accentuated.
Related Tools and Internal Resources
Haircut Finder Tool: Discover hairstyles perfectly suited to your face shape and hair type.
Eyewear Style Guide: Learn how to choose glasses frames that complement your facial features and face shape.
Makeup Contouring Techniques: Master contouring and highlighting to enhance or subtly alter the appearance of your face shape.
Personal Styling Quiz: Get personalized fashion and beauty recommendations based on your overall style preferences and features.
Body Shape Calculator: Understand your body proportions and find flattering clothing styles.
Skin Tone Analyzer: Determine your skin undertone to make better choices for makeup and clothing colors.
var chartInstance = null; // Global variable to hold chart instance
function validateInput(value, fieldId, errorId, min, max, fieldName) {
var errorElement = document.getElementById(errorId);
errorElement.style.display = 'none'; // Hide error initially
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function calculateFaceShape() {
var faceWidth = document.getElementById("faceWidth").value;
var faceHeight = document.getElementById("faceHeight").value;
var foreheadWidth = document.getElementById("foreheadWidth").value;
var jawlineLength = document.getElementById("jawlineLength").value;
var cheekboneWidth = document.getElementById("cheekboneWidth").value;
var errors = 0;
if (!validateInput(faceWidth, "faceWidth", "faceWidthError", 0, null, "Face Width")) errors++;
if (!validateInput(faceHeight, "faceHeight", "faceHeightError", 0, null, "Face Height")) errors++;
if (!validateInput(foreheadWidth, "foreheadWidth", "foreheadWidthError", 0, null, "Forehead Width")) errors++;
if (!validateInput(jawlineLength, "jawlineLength", "jawlineLengthError", 0, null, "Jawline Length")) errors++;
if (!validateInput(cheekboneWidth, "cheekboneWidth", "cheekboneWidthError", 0, null, "Cheekbone Width")) errors++;
if (errors > 0) {
document.getElementById("results").style.display = 'none';
return;
}
var fw = parseFloat(faceWidth);
var fh = parseFloat(faceHeight);
var fhw = parseFloat(foreheadWidth);
var jl = parseFloat(jawlineLength);
var cbw = parseFloat(cheekboneWidth);
var lengthWidthRatio = fh / fw;
var cheekboneRatio = cbw / fw;
var foreheadRatio = fhw / fw;
var jawlineRatio = jl / fw; // Comparing jawline measurement to overall width
var faceShape = "";
var jawlineShape = "";
var foreheadDominance = "";
// Determine Jawline Shape (simplified – based on ratio and general shape)
if (jawlineRatio 0.65) { // If jaw measurement is relatively wide compared to face width
jawlineShape = "Strong / Angular";
} else {
jawlineShape = "Rounded / Soft";
}
// Refine jawline shape based on other factors (optional, makes it more complex)
if (Math.abs(lengthWidthRatio – 1) < 0.1 && Math.abs(foreheadRatio – cheekboneRatio) < 0.1 && Math.abs(cheekboneRatio – 0.95) < 0.05) {
jawlineShape = "Angular"; // Likely square
} else if (Math.abs(lengthWidthRatio – 1) < 0.15 && Math.abs(foreheadRatio – cheekboneRatio) 1.3 && Math.abs(foreheadRatio – jawlineRatio) 0.95) {
foreheadDominance = "Forehead is the widest part.";
} else if (Math.abs(foreheadRatio – cheekboneRatio) 0.85) {
foreheadDominance = "Forehead and Cheekbones are similarly wide.";
} else if (cheekboneRatio > foreheadRatio && cheekboneRatio > jawlineRatio) {
foreheadDominance = "Cheekbones are the widest part.";
} else if (jawlineRatio > foreheadRatio && jawlineRatio > cheekboneRatio) {
foreheadDominance = "Jawline is the widest part.";
} else {
foreheadDominance = "Proportions are balanced.";
}
// Main Face Shape Logic
var tolerance = 0.1; // Tolerance for comparisons
if (Math.abs(lengthWidthRatio – 1) < tolerance && Math.abs(foreheadRatio – cheekboneRatio) < tolerance && Math.abs(cheekboneRatio – 0.95) < tolerance ) {
faceShape = "Square";
} else if (Math.abs(lengthWidthRatio – 1) < tolerance * 1.5 && Math.abs(foreheadRatio – cheekboneRatio) 1.3 && Math.abs(foreheadRatio – cheekboneRatio) < tolerance && Math.abs(cheekboneRatio – jawlineRatio) 1.3 && cheekboneRatio > foreheadRatio && foreheadRatio > jawlineRatio * 1.1) { // Cheekbones widest, forehead narrower, jawline narrowest
faceShape = "Heart";
} else if (lengthWidthRatio > 1.2 && cheekboneRatio > foreheadRatio && cheekboneRatio > jawlineRatio && Math.abs(foreheadRatio – jawlineRatio) 1.25 && cheekboneRatio > foreheadRatio && foreheadRatio > jawlineRatio * 1.1) { // Oval characteristics: longer than wide, cheekbones widest, tapering jaw
faceShape = "Oval";
} else {
// Default or fallback logic
if (lengthWidthRatio > 1.3) faceShape = "Likely Oblong or Oval";
else if (Math.abs(lengthWidthRatio – 1) 1.1) ? "Longer than wide" : (lengthWidthRatio < 0.9 ? "Wider than long" : "Length ~ Width");
var tableFaceHeightChar = ""; // Less critical on its own
var tableForeheadWidthChar = "";
if(Math.abs(fhw – cbw) < 0.2 && Math.abs(cbw – (jl*2)) cbw && fhw > (jl*2)) tableForeheadWidthChar = "Widest";
else if (cbw > fhw && cbw > (jl*2)) tableForeheadWidthChar = "Widest";
else if ((jl*2) > fhw && (jl*2) > cbw) tableForeheadWidthChar = "Widest";
else if (fhw > cbw) tableForeheadWidthChar = "Forehead wider";
else if (cbw > fhw) tableForeheadWidthChar = "Cheekbones wider";
else tableForeheadWidthChar = "Balanced";
var tableJawlineLengthChar = "";
if (Math.abs(jl*2 – fw) < 0.3) tableJawlineLengthChar = "Angular/Square";
else if (Math.abs(jl*2 – cbw) fw*0.8) tableJawlineLengthChar = "Strong Jaw";
else if (jl*2 < cbw*0.8) tableJawlineLengthChar = "Tapered/Pointed";
else tableJawlineLengthChar = "Rounded";
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document.getElementById("tableForeheadWidthChar").textContent = tableForeheadWidthChar;
document.getElementById("tableJawlineLengthChar").textContent = tableJawlineLengthChar;
document.getElementById("tableCheekboneWidth").textContent = cbw.toFixed(1) + " units";
document.getElementById("tableCheekboneWidthChar").textContent = "Widest point"; // Default, refined by logic above
// Update Chart
updateChart(fw, fh, fhw, cbw, jl * 2);
}
function updateChart(faceWidth, faceHeight, foreheadWidth, cheekboneWidth, jawlineLength) {
var ctx = document.getElementById("faceShapeChart").getContext("2d");
// Destroy previous chart instance if it exists
if (chartInstance) {
chartInstance.destroy();
}
// Define chart dimensions dynamically based on container
var chartContainer = document.getElementById('chartContainer');
var canvasWidth = chartContainer.offsetWidth * 0.9; // Use 90% of container width
var canvasHeight = canvasWidth * 0.75; // Maintain aspect ratio (e.g., 4:3)
// Set canvas dimensions directly – IMPORTANT for chart rendering
var canvas = document.getElementById('faceShapeChart');
canvas.width = canvasWidth;
canvas.height = canvasHeight;
var data = {
labels: ["Face Width", "Face Height", "Forehead", "Cheekbones", "Jawline"],
datasets: [{
label: 'Measurements',
data: [faceWidth, faceHeight, foreheadWidth, cheekboneWidth, jawlineLength],
backgroundColor: [
'rgba(0, 74, 153, 0.6)', // Face Width – Primary Blue
'rgba(40, 167, 69, 0.6)', // Face Height – Success Green
'rgba(255, 193, 7, 0.6)', // Forehead – Warning Yellow
'rgba(108, 117, 125, 0.6)',// Cheekbones – Secondary Gray
'rgba(220, 53, 69, 0.6)' // Jawline – Danger Red
],
borderColor: [
'rgba(0, 74, 153, 1)',
'rgba(40, 167, 69, 1)',
'rgba(255, 193, 7, 1)',
'rgba(108, 117, 125, 1)',
'rgba(220, 53, 69, 1)'
],
borderWidth: 1
}]
};
var options = {
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maintainAspectRatio: false, // Disable default aspect ratio to use manual dimensions
scales: {
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beginAtZero: true,
title: {
display: true,
text: 'Measurement Value (Units)'
}
},
x: {
title: {
display: true,
text: 'Facial Feature'
}
}
},
plugins: {
legend: {
display: false // Hide legend as labels are on x-axis
},
title: {
display: true,
text: 'Facial Measurement Comparison'
}
}
};
chartInstance = new Chart(ctx, {
type: 'bar',
data: data,
options: options
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}
function resetCalculator() {
document.getElementById("faceWidth").value = "";
document.getElementById("faceHeight").value = "";
document.getElementById("foreheadWidth").value = "";
document.getElementById("jawlineLength").value = "";
document.getElementById("cheekboneWidth").value = "";
document.getElementById("faceWidthError").style.display = 'none';
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document.getElementById("jawlineLengthError").style.display = 'none';
document.getElementById("cheekboneWidthError").style.display = 'none';
document.getElementById("results").style.display = 'none';
// Clear chart
var ctx = document.getElementById("faceShapeChart").getContext("2d");
if (chartInstance) {
chartInstance.destroy();
chartInstance = null;
}
// Clear canvas visually if no chart instance
canvas = document.getElementById('faceShapeChart');
canvas.getContext('2d').clearRect(0, 0, canvas.width, canvas.height);
// Clear table content
document.getElementById("tableFaceWidth").textContent = "";
document.getElementById("tableFaceHeight").textContent = "";
document.getElementById("tableForeheadWidth").textContent = "";
document.getElementById("tableCheekboneWidth").textContent = "";
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document.getElementById("tableJawlineLengthChar").textContent = "";
document.getElementById("tableCheekboneWidthChar").textContent = "";
}
function copyResults() {
var primaryShape = document.getElementById("primaryResultValue").textContent;
var lengthWidthRatio = document.getElementById("lengthWidthRatio").textContent;
var jawlineShape = document.getElementById("jawlineShapeDescription").textContent;
var foreheadDominance = document.getElementById("foreheadDominance").textContent;
var tableFaceWidth = document.getElementById("tableFaceWidth").textContent;
var tableFaceHeight = document.getElementById("tableFaceHeight").textContent;
var tableForeheadWidth = document.getElementById("tableForeheadWidth").textContent;
var tableCheekboneWidth = document.getElementById("tableCheekboneWidth").textContent;
var tableJawlineLength = document.getElementById("tableJawlineLength").textContent;
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resultsText += "Face Length vs. Width Ratio: " + lengthWidthRatio + "\n";
resultsText += "Jawline Shape: " + jawlineShape + "\n";
resultsText += "Forehead Dominance: " + foreheadDominance + "\n\n";
resultsText += "Key Measurements:\n";
resultsText += "- " + tableFaceWidth + "\n";
resultsText += "- " + tableFaceHeight + "\n";
resultsText += "- " + tableForeheadWidth + "\n";
resultsText += "- " + tableCheekboneWidth + "\n";
resultsText += "- " + tableJawlineLength + "\n\n";
resultsText += "Calculated using: [Your Website Name/Link]";
// Use navigator.clipboard for modern browsers
if (navigator.clipboard && navigator.clipboard.writeText) {
navigator.clipboard.writeText(resultsText).then(function() {
alert('Results copied to clipboard!');
}).catch(function(err) {
console.error('Async: Could not copy text: ', err);
fallbackCopyTextToClipboard(resultsText); // Fallback
});
} else {
fallbackCopyTextToClipboard(resultsText); // Fallback for older browsers
}
}
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textArea.value = text;
textArea.style.position="fixed";
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textArea.style.top="-9999px";
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var successful = document.execCommand('copy');
var msg = successful ? 'successful' : 'unsuccessful';
alert('Results copied to clipboard! (' + msg + ')');
} catch (err) {
console.error('Fallback: Oops, unable to copy', err);
alert('Could not copy results. Please copy manually.');
}
document.body.removeChild(textArea);
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// Initialize Chart.js library – Assuming it's loaded globally or via CDN
// If not, you would need to include the Chart.js library script tag before this script.
// For this exercise, we assume Chart.js is available.
// Example CDN:
// Ensure the chart is drawn when the page loads if there are default values
document.addEventListener('DOMContentLoaded', function() {
// Optionally pre-fill with example data or leave blank until calculation
// resetCalculator(); // Call reset to ensure clean state initially
// updateChart(0,0,0,0,0); // Draw an empty chart initially
});