The outcome or total (e.g., Miles, Cost, Total Words).
The input or basis (e.g., Hours, Items, Minutes).
Calculation Results
Unit Rate (Constant of Proportionality):
—
This means for every 1 unit, there are —units.
Equation: y = kx
Graph Coordinates Table
Use these points to plot your linear graph starting from the origin (0,0).
Point
X (Input)
Y (Output)
Visual Graph Representation
This visualization shows the slope of the unit rate starting from the origin.
X Axis
Y Axis
0
function calculateUnitRate() {
// 1. Get Input Values
var yVal = parseFloat(document.getElementById('urg_y_val').value);
var xVal = parseFloat(document.getElementById('urg_x_val').value);
var yLabel = document.getElementById('urg_y_label').value.trim();
var xLabel = document.getElementById('urg_x_label').value.trim();
// Default labels if empty
if (!yLabel) yLabel = "Units (y)";
if (!xLabel) xLabel = "Units (x)";
// 2. Validate Inputs
if (isNaN(yVal) || isNaN(xVal)) {
alert("Please enter valid numeric values for both quantities.");
return;
}
if (xVal === 0) {
alert("The independent quantity (x) cannot be zero when calculating a unit rate.");
return;
}
// 3. Calculate Unit Rate (k)
var k = yVal / xVal;
// Rounding for display clean-up (max 4 decimals)
var kDisplay = Math.round(k * 10000) / 10000;
// 4. Update Result Text
document.getElementById('urg_result').style.display = 'block';
document.getElementById('urg_rate_display').innerHTML = kDisplay + " " + yLabel + " / " + xLabel;
document.getElementById('urg_x_name_res').innerText = xLabel;
document.getElementById('urg_y_name_res').innerText = yLabel;
document.getElementById('urg_k_res').innerText = kDisplay;
document.getElementById('urg_slope_val').innerText = kDisplay;
// 5. Update Table Headers
document.getElementById('urg_th_x').innerText = "X (" + xLabel + ")";
document.getElementById('urg_th_y').innerText = "Y (" + yLabel + ")";
// 6. Generate Table Rows
var tableBody = document.getElementById('urg_table_body');
tableBody.innerHTML = ""; // Clear previous
// We will generate 5 points: 0, 1, 2, 5, and the original X input
var steps = [0, 1, 2, 5, xVal];
// Sort steps numerically and remove duplicates
steps.sort(function(a, b) { return a – b; });
var uniqueSteps = [];
for (var i = 0; i < steps.length; i++) {
if (i === 0 || steps[i] !== steps[i-1]) {
uniqueSteps.push(steps[i]);
}
}
for (var i = 0; i < uniqueSteps.length; i++) {
var cx = uniqueSteps[i];
var cy = cx * k;
// formatting
var cxStr = (Math.round(cx * 100) / 100).toString();
var cyStr = (Math.round(cy * 100) / 100).toString();
var row = "
(" + cxStr + ", " + cyStr + ")
" + cxStr + "
" + cyStr + "
";
tableBody.innerHTML += row;
}
// 7. Update SVG Graph
var svgGroup = document.getElementById('svg_dynamic_content');
svgGroup.innerHTML = ""; // Clear previous drawing
document.getElementById('svg_x_label').textContent = xLabel;
// We need to scale the line to fit the box (ViewBox 400×300, drawing area roughly 340×240)
// Origin is at (40, 260)
// Define max visual limits based on the input xVal and yVal provided by user to ensure the point they typed is visible
var maxX = xVal * 1.2; // Add 20% padding
var maxY = yVal * 1.2; // Add 20% padding
// Calculate scaling factors
// Width available = 340px, Height available = 240px
var scaleX = 340 / maxX;
var scaleY = 240 / maxY;
// Plot the line from (0,0) to (maxX, maxY) – purely geometrical
// y = kx. End point logic:
var endX = maxX;
var endY = endX * k;
// Convert logic coords to SVG coords
// SVG X = 40 + (valX * scaleX)
// SVG Y = 260 – (valY * scaleY)
var x1 = 40;
var y1 = 260;
var x2 = 40 + (endX * scaleX);
var y2 = 260 – (endY * scaleY);
// Draw Line
var line = document.createElementNS('http://www.w3.org/2000/svg', 'line');
line.setAttribute('x1', x1);
line.setAttribute('y1', y1);
line.setAttribute('x2', x2);
line.setAttribute('y2', y2);
line.setAttribute('class', 'graph-line');
svgGroup.appendChild(line);
// Plot the specific user point (xVal, yVal)
var px = 40 + (xVal * scaleX);
var py = 260 – (yVal * scaleY);
var circle = document.createElementNS('http://www.w3.org/2000/svg', 'circle');
circle.setAttribute('cx', px);
circle.setAttribute('cy', py);
circle.setAttribute('r', 5);
circle.setAttribute('class', 'point');
svgGroup.appendChild(circle);
// Add text label for the point
var text = document.createElementNS('http://www.w3.org/2000/svg', 'text');
text.setAttribute('x', px + 10);
text.setAttribute('y', py – 10);
text.setAttribute('class', 'label-text');
text.textContent = "(" + xVal + ", " + yVal + ")";
svgGroup.appendChild(text);
}
Understanding the Unit Rate Graph Calculator
In mathematics and physics, a Unit Rate describes how many units of the dependent quantity (usually denoted as y) correspond to exactly one unit of the independent quantity (denoted as x). This calculator is designed to help students, teachers, and professionals instantly find the unit rate, generate the linear equation, and visualize the data points required to graph the relationship.
What is a Unit Rate on a Graph?
When you graph a proportional relationship, the resulting line passes through the origin (0,0). The unit rate is visually represented as the slope of this line.
The Origin (0,0): At zero input (x), there is zero output (y).
Slope (k): The constant of proportionality. It tells you the steepness of the line.
Equation: The relationship is expressed as y = kx, where k is the unit rate.
How to Use This Calculator
Enter the Dependent Quantity (y): This is usually the "total" amount, such as Total Cost, Total Distance, or Total Items produced.
Enter the Independent Quantity (x): This is the basis of the rate, such as Hours, Minutes, or Number of Items.
Define Labels: To make your results meaningful, input the names of the units (e.g., "Miles" and "Hours").
Calculate: Click the button to see the Unit Rate, the linear equation, and a table of coordinates (x, y) that you can use to draw the graph on graph paper.
Example Calculation
Imagine you are tracking a car that travels 150 miles in 3 hours.
y (Dependent): 150 (Miles)
x (Independent): 3 (Hours)
Calculation: 150 รท 3 = 50.
Result: The unit rate is 50 Miles per Hour.
Equation:y = 50x.
Graph Point: If you go to x=1 on the graph, y will be at 50.
Why is the "Constant of Proportionality" Important?
The constant of proportionality (k) is synonymous with the unit rate. It allows you to predict outcomes for any input. If you know the unit rate is 50 miles per hour, you can easily calculate the distance for 10 hours (500 miles) or 0.5 hours (25 miles) simply by multiplying the input (x) by the constant (k).