Solar Panel Tilt Calculator
Optimize your solar energy output by finding the ideal tilt angle for your panels.
Solar Panel Tilt Calculator
Enter latitude in degrees (e.g., 34.05 for Los Angeles). Northern Hemisphere positive, Southern Hemisphere negative.
January
February
March
April
May
June
July
August
September
October
November
December
Select the month for which you want to optimize the tilt angle.
True South
True North
True East
True West
Select the direction your solar panels face. 'True South' is optimal for Northern Hemisphere, 'True North' for Southern.
Your Results
Optimal Tilt Angle:
Solar Declination:
Average Angle of Incidence:
Key Assumptions
Annual Energy Production by Tilt Angle
Chart shows estimated relative energy production at different tilt angles throughout the year.
Tilt Angle Optimization Data
| Month | Optimal Tilt (Degrees) | Estimated Relative Production (%) | Solar Declination (Degrees) |
|---|
What is Solar Panel Tilt Angle Optimization?
Optimizing the solar panel tilt angle refers to the process of determining the ideal angle at which to position your solar panels relative to the horizon to maximize the amount of sunlight they capture throughout the year, or during specific seasons. Solar panels are most efficient when sunlight strikes their surface perpendicularly. Since the sun's position in the sky changes daily and seasonally due to the Earth's axial tilt, a fixed-tilt solar panel system will not always be perfectly aligned with the sun. By adjusting the tilt angle, you can significantly improve the energy yield from your solar photovoltaic (PV) or solar thermal systems.
Who should use a solar panel tilt calculator?
- Homeowners and businesses installing new solar panels who want to maximize their electricity generation.
- Existing solar system owners looking to improve performance, perhaps by adjusting their panels seasonally.
- Solar installers and designers who need to provide accurate performance estimates to clients.
- Renewable energy enthusiasts and students learning about solar energy principles.
Common Misconceptions about Solar Panel Tilt:
- "Steeper is always better": While steeper angles are good for winter sun, they can be detrimental in summer. The optimal angle is a balance.
- "One angle fits all": The ideal tilt angle depends heavily on latitude, seasonal energy needs, and even panel orientation (due to the sun's path).
- "Seasonal adjustments are too complex": While manual seasonal adjustments require effort, a good calculator can simplify determining the best angles for different periods. Many modern systems offer automated tracking.
- "Tilt doesn't matter as much as panel quality": While panel efficiency is crucial, optimizing tilt can increase energy output by 5-15% or more annually, a significant gain.
Solar Panel Tilt Angle Formula and Mathematical Explanation
The core principle behind optimizing solar panel tilt is to position the panel to be as perpendicular as possible to the sun's rays. The sun's apparent position in the sky is influenced by two main factors: the Earth's rotation (daily cycle) and the Earth's orbit around the sun combined with its axial tilt (seasonal cycle). The solar panel tilt angle is typically optimized based on:
- Latitude (L): Your location's position north or south of the equator.
- Solar Declination (δ): The angle between the sun's rays and the plane of the Earth's equator. It varies from approximately +23.45° in summer to -23.45° in winter.
- Hour Angle (ω): The angular displacement of the sun east or west of the local meridian. This is for tracking the sun's position throughout the day, but for fixed tilt optimization, we often consider average daily or monthly positions.
- Panel Orientation: The azimuth angle (direction the panel faces).
For a fixed-tilt system aiming for year-round optimal performance, a common rule of thumb is to set the tilt angle equal to the latitude. However, to maximize energy production during specific seasons, adjustments are made.
Simplified Formula for Optimal Tilt (Year-Round):
Optimal Tilt Angle (β) ≈ Latitude (L)
This provides a good average, but is not ideal for maximizing seasonal output.
Formula for Optimal Tilt (Seasonal Optimization):
To maximize energy capture during a specific month or season, the ideal tilt angle (β) aims to make the panel's angle perpendicular to the sun's rays at solar noon.
β ≈ |Latitude (L) – Solar Declination (δ)|
Where:
- β (Beta): The solar panel tilt angle from the horizontal (in degrees).
- L (Latitude): Your location's latitude in degrees. Positive for Northern Hemisphere, negative for Southern.
- δ (Delta): The solar declination angle for the specific day or average for the month (in degrees).
Calculating Solar Declination (δ):
A common approximation for solar declination (δ) on day 'n' of the year (where n=1 is January 1st) is:
δ = 23.45 * sin( (360/365) * (n + 284) ) (in degrees)
Note: The 'n + 284' offset ensures correct phase alignment with the seasons.
Angle of Incidence Calculation:
The angle of incidence (θ) is the angle between the sun's rays and the normal (perpendicular line) to the solar panel surface. Lower angles of incidence mean more direct sunlight.
θ = arccos( cos(L – β) * cos(δ) + sin(L – β) * sin(δ) * cos(A_s – A_panel) )
Where:
- L is Latitude
- β is Tilt Angle
- δ is Solar Declination
- A_s is Solar Azimuth Angle (0° at solar noon)
- A_panel is Panel Azimuth Angle (0° for South-facing in NH, North-facing in SH)
For simplicity in this calculator, we often focus on the solar noon angle of incidence, where the solar azimuth angle is 0.
Table of Variables:
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| Latitude (L) | Angular distance north or south of the equator | Degrees | -90° to +90° |
| Solar Declination (δ) | Angle between sun's rays and Earth's equatorial plane | Degrees | -23.45° to +23.45° |
| Tilt Angle (β) | Angle of the panel from the horizontal | Degrees | 0° to 90° |
| Panel Orientation (Azimuth) | Direction the panel faces (0°=South/North, 90°=East, -90°=West) | Degrees | -180° to +180° |
| Angle of Incidence (θ) | Angle between sun's rays and panel normal | Degrees | 0° to 90° (lower is better) |
| Day of Year (n) | Sequential day number from Jan 1st | Integer | 1 to 365 |
Practical Examples (Real-World Use Cases)
Example 1: Maximizing Winter Energy for a Homeowner in Chicago
- Location: Chicago, Illinois, USA
- Latitude (L): Approximately 41.88° N
- Target Month: January (Winter)
- Panel Orientation: True South
Inputs for Calculator:
- Latitude: 41.88
- Month: January (1)
- Panel Orientation: True South
Calculator Output (Estimated):
- Optimal Tilt Angle: ~55-60°
- Solar Declination (Jan avg): ~ -20°
- Estimated Relative Production Increase: ~15-20% compared to latitude tilt.
Interpretation: For Chicago in January, a steeper tilt angle than the latitude (~42°) is needed to capture the lower winter sun more directly. This maximizes electricity generation during the month with the least sunlight and potentially highest heating demand.
Example 2: Year-Round Optimization for a Commercial Installation in Sydney
- Location: Sydney, Australia
- Latitude (L): Approximately -33.87° S
- Target: Year-round average performance
- Panel Orientation: True North (optimal for Southern Hemisphere)
Inputs for Calculator:
- Latitude: -33.87
- Month: Choose July (mid-winter in SH) or average across months (calculator provides monthly view). Let's use July for calculation.
- Panel Orientation: True North
Calculator Output (Estimated for July):
- Optimal Tilt Angle: ~35-40° (adjusting for latitude and solar declination)
- Solar Declination (July avg): ~ +18°
- Estimated Relative Production Increase: ~10-15% compared to flat tilt.
Interpretation: For Sydney, the optimal tilt is influenced by the southern latitude. While a latitude-based tilt (~34°) is a good starting point for year-round performance, calculating for specific months like July (winter) shows a slightly higher optimal angle to catch the lower sun. The calculator helps visualize this monthly variation. For year-round optimization, often the latitude tilt is chosen for simplicity, or a slightly lower angle if summer sun is prioritized.
How to Use This Solar Panel Tilt Calculator
Our Solar Panel Tilt Calculator is designed to be intuitive and provide actionable insights for optimizing your solar energy system. Follow these simple steps:
- Enter Your Latitude: Locate your property on a map and find its latitude. Input this value in degrees. Remember, positive values are for the Northern Hemisphere, and negative values are for the Southern Hemisphere.
- Select the Month: Choose the month for which you want to optimize the tilt angle. This is crucial because the sun's position changes significantly throughout the year. Selecting a winter month will suggest a steeper angle, while a summer month will suggest a shallower angle.
- Choose Panel Orientation: Specify the direction your solar panels face (azimuth). For the Northern Hemisphere, "True South" is generally best. For the Southern Hemisphere, "True North" is optimal. East and West orientations are also options but will produce less energy overall.
- Calculate: Click the "Calculate Optimal Tilt" button.
How to Read the Results:
- Optimal Tilt Angle: This is the primary result – the angle in degrees from the horizontal that your panels should be set to maximize solar absorption for the selected month and location.
- Intermediate Values:
- Solar Declination: Shows the sun's angle relative to the Earth's equator for that month.
- Average Angle of Incidence: A measure of how directly sunlight hits the panel surface. Lower is better.
- Main Highlighted Result: The "Optimal Tilt Angle" is prominently displayed, often as the main takeaway.
- Formula Explanation: A brief overview of the calculation method used is provided for transparency.
- Assumptions: Lists key factors considered, such as perfect panel orientation and clear sky conditions.
Decision-Making Guidance:
- Fixed vs. Seasonal Tilt: If your system allows for manual adjustments, use the calculator to determine the best angle for the current season. Adjusting twice a year (e.g., spring/autumn) is common.
- Year-Round Compromise: If seasonal adjustments aren't feasible, setting the tilt angle equal to your latitude often provides the best overall annual energy production.
- Compare Monthly Values: Use the monthly options to understand the seasonal variations and choose a compromise angle if needed.
- Impact on Installation: Discuss these optimal angles with your solar installer to ensure the mounting system can accommodate the desired angles.
Key Factors That Affect Solar Panel Tilt Results
While the latitude and month are primary inputs, several other factors influence the true optimal tilt angle and overall solar energy production:
- Latitude: This is the most significant factor. Locations closer to the equator have a more direct sun path year-round, requiring less extreme tilt angles. Polar regions require much steeper angles, especially in winter.
- Seasonal Energy Needs: Do you need more power in winter (for heating) or summer (for air conditioning)? Optimizing for winter requires a steeper tilt; optimizing for summer requires a shallower tilt. Our calculator helps by letting you select the month.
- Panel Orientation (Azimuth): Panels facing true south (in the Northern Hemisphere) or true north (in the Southern Hemisphere) receive the most direct sunlight throughout the day. East-facing panels peak in the morning, and west-facing panels peak in the afternoon. The calculator accounts for this, though South/North orientation yields the highest overall production. An imperfect azimuth angle significantly impacts output.
- Shading and Obstructions: Trees, buildings, or other obstructions can cast shadows on panels, drastically reducing their output. The ideal tilt angle should also consider avoiding shade, especially during peak sun hours. This calculator assumes no shading.
- Weather Patterns and Cloud Cover: Regions with frequent cloud cover might benefit from tilt angles that perform better under diffuse light conditions, though direct sunlight optimization is still primary. Seasonal cloud patterns can influence the best compromise angle.
- Local Climate and Snowfall: In snowy regions, a steeper tilt angle (e.g., >40-45°) helps snow slide off the panels more easily, preventing prolonged periods of reduced or zero energy production during winter months.
- Fixed vs. Tracking Systems: This calculator primarily addresses fixed-tilt systems. Solar trackers automatically adjust the panel's orientation and tilt throughout the day and year to follow the sun, achieving significantly higher energy yields (up to 25-40% more) but at a higher cost and complexity.
- Installation Constraints: Roof pitch, available space, and structural limitations might prevent achieving the mathematically optimal tilt angle. A practical compromise is often necessary.
Frequently Asked Questions (FAQ)
What is the difference between solar panel tilt and azimuth?
Tilt is the angle of the panel relative to the horizontal ground (0° is flat, 90° is vertical). Azimuth is the compass direction the panel faces (0° is typically South in the Northern Hemisphere, 180° North in the Southern Hemisphere; 90° is East, 270° West). Both are critical for maximizing solar energy capture.
Is it worth adjusting my solar panels seasonally?
For fixed-mount systems, seasonal adjustments can increase annual energy yield by 5-15%. If you can easily adjust the tilt (e.g., ground mounts or certain roof mounts), it can be beneficial, especially if you have distinct seasonal energy needs.
What is the 'best' tilt angle for year-round performance?
A common rule of thumb for year-round performance is to set the tilt angle equal to your location's latitude. However, optimizing based on the monthly calculator results and choosing a compromise angle (often slightly steeper than latitude for winter bias) can yield slightly better results.
Do I need to worry about tilt angle in the Southern Hemisphere?
Yes, the principles are the same, but the optimal orientation shifts. In the Southern Hemisphere, panels should ideally face True North, and the tilt angle calculations adjust accordingly based on the negative latitude value.
How does tilt angle affect solar thermal (water heating) panels?
The principles are similar, but solar thermal panels often benefit from slightly steeper angles than PV panels, especially in colder climates, to aid in drainage and reduce snow accumulation, while still capturing maximum solar radiation.
Can I use the calculator if my latitude is 0 (on the equator)?
Yes. If your latitude is 0, the optimal tilt angle will closely follow the solar declination angle, changing significantly between summer (+23.45°) and winter (-23.45°). You'll likely want to adjust seasonally or find a compromise angle near flat.
What is solar declination and why is it important?
Solar declination is the angle between the sun's rays and the Earth's equatorial plane. It varies throughout the year due to the Earth's axial tilt, causing the sun's path across the sky to be higher in summer and lower in winter. It's crucial for calculating the sun's angle relative to your panel's tilt.
Does roof pitch automatically set my solar panel tilt?
Often, yes. If your panels are mounted flush with a sloped roof, their tilt angle is determined by the roof's pitch. You might need mounting hardware (rails, tilt legs) to adjust the angle away from the roof pitch if optimal performance is critical and feasible.
How does the calculator estimate energy production?
The chart and table show *relative* energy production. They are based on models that estimate the angle of incidence of solar radiation on the panel surface at different tilt angles and times of year. Higher relative production percentages indicate more direct sunlight capture compared to other angles for that location and time. It doesn't predict absolute kWh without knowing system size and local solar irradiance data.
Location Latitude: " + latitude.toFixed(2) + "°
";
assumptionsList.innerHTML += "Target Month: " + monthSelect.options[monthSelect.selectedIndex].text + "
";
assumptionsList.innerHTML += "Panel Orientation: " + panelOrientation.charAt(0).toUpperCase() + panelOrientation.slice(1) + "
";
assumptionsList.innerHTML += "Calculation assumes solar noon conditions.
";
assumptionsList.innerHTML += "Relative production is estimated based on angle of incidence.
";
document.getElementById("assumptions").style.display = "block";
document.getElementById("results-section").style.display = "block";
// — Update Table —
updateTiltTable(normalizedProductionData, optimalTilt, latitude, solarDeclination, panelOrientation);
// — Update Chart —
updateChart(normalizedProductionData, optimalTilt, panelOrientation);
}
function updateTiltTable(data, optimalTilt, latitude, solarDeclination, panelOrientation) {
var tableBody = document.getElementById("tiltDataTable").getElementsByTagName("tbody")[0];
tableBody.innerHTML = ""; // Clear previous rows
var monthNames = ["January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December"];
var monthIndex = parseInt(document.getElementById("month").value) – 1;
var currentMonthName = monthNames[monthIndex];
// Add a row for the calculated optimal tilt for the selected month
var optimalRowData = {
tilt: optimalTilt,
production: 100, // Assume optimal is 100% for the selected month
aoi: calculateAngleOfIncidence(latitude, optimalTilt, solarDeclination, normalizeOrientation(panelOrientation))
};
// Add rows for standard tilts tested
var standardTilts = [0, 15, 30, 45, 60, 75, 90];
var otherProductionData = [];
for (var i = 0; i < standardTilts.length; i++) {
var tilt = standardTilts[i];
var aoi = calculateAngleOfIncidence(latitude, tilt, solarDeclination, normalizeOrientation(panelOrientation));
var production = estimateRelativeProduction(aoi);
otherProductionData.push({ tilt: tilt, aoi: aoi, production: production });
}
// Find max production from all calculated points (including optimal)
var allProductionValues = [optimalRowData.production];
for (var i = 0; i ({
tilt: item.tilt,
production: (item.production / maxOverallProduction) * 100,
aoi: item.aoi
}));
// Combine and sort data for the table
var tableData = [normalizedOptimalRow, …normalizedOtherData];
tableData.sort(function(a, b) { return a.tilt – b.tilt; });
// Add the optimal tilt row first, then other tilts sorted
var rowOptimal = tableBody.insertRow();
rowOptimal.insertCell().textContent = currentMonthName;
rowOptimal.insertCell().textContent = optimalTilt.toFixed(1) + "°";
rowOptimal.insertCell().textContent = "100%"; // Optimal is baseline
rowOptimal.insertCell().textContent = solarDeclination.toFixed(1) + "°";
// Add rows for standard tilts tested
for (var i = 0; i item.tilt);
var productions = data.map(item => item.production);
// Find min/max for scaling
var tiltMin = Math.min(…tilts);
var tiltMax = Math.max(…tilts);
var prodMin = 0; // Always start production from 0
var prodMax = Math.max(…productions) * 1.1; // Add some padding
// — Drawing —
var padding = 40;
var chartWidth = ctx.canvas.width – 2 * padding;
var chartHeight = ctx.canvas.height – 2 * padding;
// Y-axis (Production)
ctx.beginPath();
ctx.moveTo(padding, ctx.canvas.height – padding);
ctx.lineTo(padding, padding);
ctx.strokeStyle = '#ccc';
ctx.stroke();
// Draw Y-axis labels and ticks
var numYTicks = 5;
var yTickStep = chartHeight / numYTicks;
ctx.textAlign = 'right';
ctx.textBaseline = 'middle';
ctx.fillStyle = '#333';
for (var i = 0; i 1 ? numXTicks – 1 : 1);
for (var i = 0; i < numXTicks; i++) {
var x = padding + i * xTickStep;
ctx.fillText(tilts[i].toFixed(0) + "°", x, ctx.canvas.height – padding + 10);
ctx.moveTo(x, ctx.canvas.height – padding);
ctx.lineTo(x, ctx.canvas.height – padding – 5);
ctx.stroke();
}
// Draw the data line (Relative Production)
ctx.beginPath();
ctx.moveTo(padding, ctx.canvas.height – padding); // Start at 0 production point
for (var i = 0; i < tilts.length; i++) {
var x = padding + ((tilts[i] – tiltMin) / (tiltMax – tiltMin || 1)) * chartWidth;
var y = ctx.canvas.height – padding – ((productions[i] – prodMin) / (prodMax – prodMin || 1)) * chartHeight;
if (i === 0) {
ctx.moveTo(x, y);
} else {
ctx.lineTo(x, y);
}
}
ctx.strokeStyle = 'var(–primary-color)';
ctx.lineWidth = 2;
ctx.stroke();
// Draw points
ctx.fillStyle = 'var(–primary-color)';
for (var i = 0; i < tilts.length; i++) {
var x = padding + ((tilts[i] – tiltMin) / (tiltMax – tiltMin || 1)) * chartWidth;
var y = ctx.canvas.height – padding – ((productions[i] – prodMin) / (prodMax – prodMin || 1)) * chartHeight;
ctx.beginPath();
ctx.arc(x, y, 4, 0, 2 * Math.PI);
ctx.fill();
}
// Mark the optimal tilt point
var optimalX = padding + ((optimalTilt – tiltMin) / (tiltMax – tiltMin || 1)) * chartWidth;
var optimalY = ctx.canvas.height – padding – ((100 – prodMin) / (prodMax – prodMin || 1)) * chartHeight; // Assuming optimal is 100%
ctx.fillStyle = 'var(–success-color)';
ctx.beginPath();
ctx.arc(optimalX, optimalY, 6, 0, 2 * Math.PI);
ctx.fill();
// Add legend
ctx.textAlign = 'left';
ctx.textBaseline = 'top';
ctx.fillStyle = '#333';
ctx.font = '12px Arial';
ctx.fillText('Relative Energy Production (%)', padding, padding + 5);
ctx.fillStyle = 'var(–primary-color)';
ctx.fillRect(padding + 120, padding + 5, 10, 10);
ctx.fillText('Production Curve', padding + 135, padding + 5);
ctx.fillStyle = 'var(–success-color)';
ctx.fillRect(padding + 120, padding + 25, 10, 10);
ctx.fillText('Optimal Tilt (' + optimalTilt.toFixed(1) + '°)', padding + 135, padding + 25);
// Save the chart instance (if using a library) or just know it's drawn.
// For native canvas, we don't store an instance like Chart.js.
}
// — Reset Function —
function resetCalculator() {
document.getElementById("latitude").value = "";
document.getElementById("month").value = "1"; // Default to January
document.getElementById("panelOrientation").value = "south"; // Default to South
// Clear errors
document.getElementById("latitude-error").style.display = "none";
document.getElementById("month-error").style.display = "none";
document.getElementById("orientation-error").style.display = "none";
// Hide results
document.getElementById("results-section").style.display = "none";
// Clear table and chart (optional, or recalculate with defaults)
document.getElementById("tiltDataTable").getElementsByTagName("tbody")[0].innerHTML = "";
var ctx = document.getElementById('tiltEnergyChart').getContext('2d');
ctx.clearRect(0, 0, ctx.canvas.width, ctx.canvas.height);
}
// — Copy Results Function —
function copyResults() {
var mainResult = document.getElementById("main-result").textContent;
var optimalTiltText = document.getElementById("optimal-tilt-label").textContent + " " + document.getElementById("optimal-tilt").textContent;
var solarDeclinationText = document.getElementById("solar-declination-label").textContent + " " + document.getElementById("solar-declination").textContent;
var incidenceAngleText = document.getElementById("angle-of-incidence-label").textContent + " " + document.getElementById("angle-of-incidence").textContent;
var assumptionsDiv = document.getElementById("assumptions-list");
var assumptions = [];
var assumptionSpans = assumptionsDiv.getElementsByTagName("div");
for (var i = 0; i < assumptionSpans.length; i++) {
assumptions.push(assumptionSpans[i].textContent);
}
var formula = document.getElementById("formula-explanation").textContent;
var copyText = "— Solar Panel Tilt Calculation Results —\n\n";
copyText += "Optimal Tilt Angle: " + mainResult + "\n";
copyText += optimalTiltText + "\n";
copyText += solarDeclinationText + "\n";
copyText += incidenceAngleText + "\n\n";
copyText += "Formula Used: " + formula + "\n\n";
copyText += "Key Assumptions:\n";
for (var i = 0; i < assumptions.length; i++) {
copyText += "- " + assumptions[i] + "\n";
}
// Use navigator.clipboard if available, otherwise fallback
if (navigator.clipboard && navigator.clipboard.writeText) {
navigator.clipboard.writeText(copyText).then(function() {
// Optional: show a confirmation message
alert("Results copied to clipboard!");
}).catch(function(err) {
console.error("Failed to copy text: ", err);
fallbackCopyTextToClipboard(copyText);
});
} else {
fallbackCopyTextToClipboard(copyText);
}
}
function fallbackCopyTextToClipboard(text) {
var textArea = document.createElement("textarea");
textArea.value = text;
// Avoid flashing the whitespace in mobile browser
textArea.style.position = "fixed";
textArea.style.left = "-9999px";
textArea.style.top = "-9999px";
document.body.appendChild(textArea);
textArea.focus();
textArea.select();
try {
var successful = document.execCommand('copy');
var msg = successful ? 'successful' : 'unsuccessful';
// alert('Fallback: Copying text command was ' + msg);
if(successful) alert("Results copied to clipboard!");
} catch (err) {
console.error('Fallback: Oops, unable to copy', err);
alert("Failed to copy results. Please copy manually.");
}
document.body.removeChild(textArea);
}
// — FAQ Functionality —
function setupFaq() {
var questions = document.getElementsByClassName("faq-question");
for (var i = 0; i < questions.length; i++) {
questions[i].addEventListener("click", function() {
var answer = this.nextElementSibling; // The answer is the next sibling element
if (answer.style.display === "block") {
answer.style.display = "none";
} else {
answer.style.display = "block";
}
});
}
}
// — Initial Setup —
// Add event listeners for input changes to update results in real-time
var inputs = document.querySelectorAll("#calculator-inputs input, #calculator-inputs select");
for (var i = 0; i < inputs.length; i++) {
inputs[i].addEventListener("input", function() {
// Only calculate if all necessary fields have values
var lat = document.getElementById("latitude").value;
var month = document.getElementById("month").value;
var orientation = document.getElementById("panelOrientation").value;
if (lat && month && orientation) {
calculateTilt();
} else {
// Optionally hide results if inputs are incomplete
document.getElementById("results-section").style.display = "none";
}
});
}
// Call setupFaq when the DOM is ready
document.addEventListener("DOMContentLoaded", function() {
setupFaq();
// Optional: Trigger initial calculation if default values are set
// calculateTilt();
});