This calculator helps you find missing properties of a triangle, such as area, perimeter, or side lengths, given some of its known values. You can input two sides and an angle, or three sides, or other combinations, depending on what type of triangle you are working with (though this calculator primarily focuses on general triangles where side lengths and angles can be calculated using basic trigonometric principles and Heron's formula).
Results:
function calculateTriangle() {
var sideA = parseFloat(document.getElementById("sideA").value);
var sideB = parseFloat(document.getElementById("sideB").value);
var sideC = parseFloat(document.getElementById("sideC").value);
var angleA_deg = parseFloat(document.getElementById("angleA").value);
var angleB_deg = parseFloat(document.getElementById("angleB").value);
var angleC_deg = parseFloat(document.getElementById("angleC").value);
var area = "";
var perimeter = "";
var unknownSides = "";
var unknownAngles = "";
var inputsProvided = {
sideA: !isNaN(sideA),
sideB: !isNaN(sideB),
sideC: !isNaN(sideC),
angleA: !isNaN(angleA_deg),
angleB: !isNaN(angleB_deg),
angleC: !isNaN(angleC_deg)
};
var numSidesKnown = (inputsProvided.sideA ? 1 : 0) + (inputsProvided.sideB ? 1 : 0) + (inputsProvided.sideC ? 1 : 0);
var numAnglesKnown = (inputsProvided.angleA ? 1 : 0) + (inputsProvided.angleB ? 1 : 0) + (inputsProvided.angleC ? 1 : 0);
// Helper function to convert degrees to radians
function degToRad(degrees) {
return degrees * Math.PI / 180;
}
// Helper function to convert radians to degrees
function radToDeg(radians) {
return radians * 180 / Math.PI;
}
// — Calculations —
// Area calculation using Heron's formula if 3 sides are known
if (numSidesKnown === 3 && !isNaN(sideA) && !isNaN(sideB) && !isNaN(sideC)) {
var s = (sideA + sideB + sideC) / 2;
var calculatedArea = Math.sqrt(s * (s – sideA) * (s – sideB) * (s – sideC));
if (!isNaN(calculatedArea)) {
area = "Area: " + calculatedArea.toFixed(2);
}
}
// Area calculation using 1/2 * ab * sin(C) if 2 sides and included angle are known
else if (inputsProvided.sideA && inputsProvided.sideB && inputsProvided.angleC && numSidesKnown === 2 && numAnglesKnown === 1) {
var angleC_rad = degToRad(angleC_deg);
var calculatedArea = 0.5 * sideA * sideB * Math.sin(angleC_rad);
if (!isNaN(calculatedArea)) {
area = "Area: " + calculatedArea.toFixed(2);
}
} else if (inputsProvided.sideA && inputsProvided.sideC && inputsProvided.angleB && numSidesKnown === 2 && numAnglesKnown === 1) {
var angleB_rad = degToRad(angleB_deg);
var calculatedArea = 0.5 * sideA * sideC * Math.sin(angleB_rad);
if (!isNaN(calculatedArea)) {
area = "Area: " + calculatedArea.toFixed(2);
}
} else if (inputsProvided.sideB && inputsProvided.sideC && inputsProvided.angleA && numSidesKnown === 2 && numAnglesKnown === 1) {
var angleA_rad = degToRad(angleA_deg);
var calculatedArea = 0.5 * sideB * sideC * Math.sin(angleA_rad);
if (!isNaN(calculatedArea)) {
area = "Area: " + calculatedArea.toFixed(2);
}
}
// Perimeter calculation if 3 sides are known
if (numSidesKnown === 3 && !isNaN(sideA) && !isNaN(sideB) && !isNaN(sideC)) {
perimeter = "Perimeter: " + (sideA + sideB + sideC).toFixed(2);
}
// Calculate missing sides and angles
var calculatedSideA = !isNaN(sideA) ? sideA : NaN;
var calculatedSideB = !isNaN(sideB) ? sideB : NaN;
var calculatedSideC = !isNaN(sideC) ? sideC : NaN;
var calculatedAngleA = !isNaN(angleA_deg) ? angleA_deg : NaN;
var calculatedAngleB = !isNaN(angleB_deg) ? angleB_deg : NaN;
var calculatedAngleC = !isNaN(angleC_deg) ? angleC_deg : NaN;
// — Solve for unknown sides/angles based on input combinations —
// Case: ASA (Angle-Side-Angle)
if (numAnglesKnown === 2 && numSidesKnown === 1) {
if (inputsProvided.angleA && inputsProvided.angleB && inputsProvided.sideC) {
calculatedAngleC = 180 – angleA_deg – angleB_deg;
if (!isNaN(calculatedAngleC)) {
unknownAngles += "Angle C: " + calculatedAngleC.toFixed(2) + "° ";
var angleC_rad = degToRad(calculatedAngleC);
var angleA_rad = degToRad(angleA_deg);
calculatedSideA = sideC * Math.sin(angleA_rad) / Math.sin(angleC_rad);
unknownSides += "Side A: " + calculatedSideA.toFixed(2) + " ";
calculatedSideB = sideC * Math.sin(angleB_deg) / Math.sin(angleC_rad);
unknownSides += "Side B: " + calculatedSideB.toFixed(2) + " ";
}
} else if (inputsProvided.angleA && inputsProvided.angleC && inputsProvided.sideB) {
calculatedAngleB = 180 – angleA_deg – angleC_deg;
if (!isNaN(calculatedAngleB)) {
unknownAngles += "Angle B: " + calculatedAngleB.toFixed(2) + "° ";
var angleB_rad = degToRad(calculatedAngleB);
var angleA_rad = degToRad(angleA_deg);
calculatedSideA = sideB * Math.sin(angleA_rad) / Math.sin(angleB_rad);
unknownSides += "Side A: " + calculatedSideA.toFixed(2) + " ";
calculatedSideC = sideB * Math.sin(angleC_deg) / Math.sin(angleB_rad);
unknownSides += "Side C: " + calculatedSideC.toFixed(2) + " ";
}
} else if (inputsProvided.angleB && inputsProvided.angleC && inputsProvided.sideA) {
calculatedAngleA = 180 – angleB_deg – angleC_deg;
if (!isNaN(calculatedAngleA)) {
unknownAngles += "Angle A: " + calculatedAngleA.toFixed(2) + "° ";
var angleA_rad = degToRad(calculatedAngleA);
var angleB_rad = degToRad(angleB_deg);
calculatedSideB = sideA * Math.sin(angleB_rad) / Math.sin(angleA_rad);
unknownSides += "Side B: " + calculatedSideB.toFixed(2) + " ";
calculatedSideC = sideA * Math.sin(angleC_deg) / Math.sin(angleA_rad);
unknownSides += "Side C: " + calculatedSideC.toFixed(2) + " ";
}
}
}
// Case: SAS (Side-Angle-Side)
if (numSidesKnown === 2 && numAnglesKnown === 1) {
if (inputsProvided.sideA && inputsProvided.sideB && inputsProvided.angleC) {
var angleC_rad = degToRad(angleC_deg);
// Use Law of Cosines to find side C
calculatedSideC = Math.sqrt(sideA * sideA + sideB * sideB – 2 * sideA * sideB * Math.cos(angleC_rad));
if (!isNaN(calculatedSideC)) {
unknownSides += "Side C: " + calculatedSideC.toFixed(2) + " ";
// Use Law of Sines to find angles A and B
var angleA_rad = Math.asin((sideA * Math.sin(angleC_rad)) / calculatedSideC);
calculatedAngleA = radToDeg(angleA_rad);
unknownAngles += "Angle A: " + calculatedAngleA.toFixed(2) + "° ";
calculatedAngleB = 180 – calculatedAngleC – calculatedAngleA;
unknownAngles += "Angle B: " + calculatedAngleB.toFixed(2) + "° ";
}
} else if (inputsProvided.sideA && inputsProvided.sideC && inputsProvided.angleB) {
var angleB_rad = degToRad(angleB_deg);
calculatedSideB = Math.sqrt(sideA * sideA + sideC * sideC – 2 * sideA * sideC * Math.cos(angleB_rad));
if (!isNaN(calculatedSideB)) {
unknownSides += "Side B: " + calculatedSideB.toFixed(2) + " ";
var angleA_rad = Math.asin((sideA * Math.sin(angleB_rad)) / calculatedSideB);
calculatedAngleA = radToDeg(angleA_rad);
unknownAngles += "Angle A: " + calculatedAngleA.toFixed(2) + "° ";
calculatedAngleC = 180 – calculatedAngleA – calculatedAngleB;
unknownAngles += "Angle C: " + calculatedAngleC.toFixed(2) + "° ";
}
} else if (inputsProvided.sideB && inputsProvided.sideC && inputsProvided.angleA) {
var angleA_rad = degToRad(angleA_deg);
calculatedSideA = Math.sqrt(sideB * sideB + sideC * sideC – 2 * sideB * sideC * Math.cos(angleA_rad));
if (!isNaN(calculatedSideA)) {
unknownSides += "Side A: " + calculatedSideA.toFixed(2) + " ";
var angleB_rad = Math.asin((sideB * Math.sin(angleA_rad)) / calculatedSideA);
calculatedAngleB = radToDeg(angleB_rad);
unknownAngles += "Angle B: " + calculatedAngleB.toFixed(2) + "° ";
calculatedAngleC = 180 – calculatedAngleA – calculatedAngleB;
unknownAngles += "Angle C: " + calculatedAngleC.toFixed(2) + "° ";
}
}
}
// Case: SSS (Side-Side-Side)
if (numSidesKnown === 3 && numAnglesKnown === 0) {
if (!isNaN(sideA) && !isNaN(sideB) && !isNaN(sideC)) {
// Check triangle inequality theorem
if (sideA + sideB > sideC && sideA + sideC > sideB && sideB + sideC > sideA) {
var angleA_rad = Math.acos((sideB * sideB + sideC * sideC – sideA * sideA) / (2 * sideB * sideC));
calculatedAngleA = radToDeg(angleA_rad);
unknownAngles += "Angle A: " + calculatedAngleA.toFixed(2) + "° ";
var angleB_rad = Math.acos((sideA * sideA + sideC * sideC – sideB * sideB) / (2 * sideA * sideC));
calculatedAngleB = radToDeg(angleB_rad);
unknownAngles += "Angle B: " + calculatedAngleB.toFixed(2) + "° ";
calculatedAngleC = 180 – calculatedAngleA – calculatedAngleB;
unknownAngles += "Angle C: " + calculatedAngleC.toFixed(2) + "° ";
} else {
unknownAngles = "Invalid triangle: Side lengths do not satisfy triangle inequality.";
}
}
}
// Case: AAS (Angle-Angle-Side)
if (numAnglesKnown === 2 && numSidesKnown === 1) {
if (inputsProvided.angleA && inputsProvided.angleB && inputsProvided.sideA) {
calculatedAngleC = 180 – angleA_deg – angleB_deg;
if (!isNaN(calculatedAngleC)) {
unknownAngles += "Angle C: " + calculatedAngleC.toFixed(2) + "° ";
var angleC_rad = degToRad(calculatedAngleC);
var angleB_rad = degToRad(angleB_deg);
calculatedSideB = sideA * Math.sin(angleB_rad) / Math.sin(degToRad(angleA_deg));
unknownSides += "Side B: " + calculatedSideB.toFixed(2) + " ";
calculatedSideC = sideA * Math.sin(angleC_rad) / Math.sin(degToRad(angleA_deg));
unknownSides += "Side C: " + calculatedSideC.toFixed(2) + " ";
}
} else if (inputsProvided.angleA && inputsProvided.angleC && inputsProvided.sideA) {
calculatedAngleB = 180 – angleA_deg – angleC_deg;
if (!isNaN(calculatedAngleB)) {
unknownAngles += "Angle B: " + calculatedAngleB.toFixed(2) + "° ";
var angleB_rad = degToRad(calculatedAngleB);
var angleC_rad = degToRad(angleC_deg);
calculatedSideB = sideA * Math.sin(angleB_rad) / Math.sin(degToRad(angleA_deg));
unknownSides += "Side B: " + calculatedSideB.toFixed(2) + " ";
calculatedSideC = sideA * Math.sin(angleC_rad) / Math.sin(degToRad(angleA_deg));
unknownSides += "Side C: " + calculatedSideC.toFixed(2) + " ";
}
} else if (inputsProvided.angleB && inputsProvided.angleC && inputsProvided.sideB) {
calculatedAngleA = 180 – angleB_deg – angleC_deg;
if (!isNaN(calculatedAngleA)) {
unknownAngles += "Angle A: " + calculatedAngleA.toFixed(2) + "° ";
var angleA_rad = degToRad(calculatedAngleA);
var angleC_rad = degToRad(angleC_deg);
calculatedSideA = sideB * Math.sin(angleA_rad) / Math.sin(degToRad(angleB_deg));
unknownSides += "Side A: " + calculatedSideA.toFixed(2) + " ";
calculatedSideC = sideB * Math.sin(angleC_rad) / Math.sin(degToRad(angleB_deg));
unknownSides += "Side C: " + calculatedSideC.toFixed(2) + " ";
}
}
}
// Case: SSA (Side-Side-Angle) – Ambiguous case, this calculator will try to find one solution.
// A full implementation for SSA is complex as it can yield 0, 1, or 2 triangles.
// This simplified version will calculate based on the first possible scenario.
if (numSidesKnown === 2 && numAnglesKnown === 1) {
if (inputsProvided.sideA && inputsProvided.sideB && inputsProvided.angleA) {
var angleA_rad = degToRad(angleA_deg);
var ratio = (sideA * Math.sin(angleA_rad)) / sideB;
if (ratio > 1) {
unknownAngles = "No triangle possible.";
} else {
var angleB_rad = Math.asin(ratio);
var angleB_deg_sol1 = radToDeg(angleB_rad);
var angleC_deg_sol1 = 180 – angleA_deg – angleB_deg_sol1;
var sideC_sol1 = (sideB * Math.sin(degToRad(angleC_deg_sol1))) / Math.sin(angleA_rad);
unknownAngles = "Angle B: " + angleB_deg_sol1.toFixed(2) + "°, ";
unknownAngles += "Angle C: " + angleC_deg_sol1.toFixed(2) + "°, ";
unknownSides = "Side C: " + sideC_sol1.toFixed(2);
// Check for a second possible triangle
var angleB_deg_sol2 = 180 – angleB_deg_sol1;
if (angleB_deg_sol2 > 0 && angleA_deg + angleB_deg_sol2 1) {
unknownAngles = "No triangle possible.";
} else {
var angleC_rad = Math.asin(ratio);
var angleC_deg_sol1 = radToDeg(angleC_rad);
var angleB_deg_sol1 = 180 – angleA_deg – angleC_deg_sol1;
var sideB_sol1 = (sideC * Math.sin(degToRad(angleB_deg_sol1))) / Math.sin(angleA_rad);
unknownAngles = "Angle C: " + angleC_deg_sol1.toFixed(2) + "°, ";
unknownAngles += "Angle B: " + angleB_deg_sol1.toFixed(2) + "°, ";
unknownSides = "Side B: " + sideB_sol1.toFixed(2);
// Check for a second possible triangle
var angleC_deg_sol2 = 180 – angleC_deg_sol1;
if (angleC_deg_sol2 > 0 && angleA_deg + angleC_deg_sol2 1) {
unknownAngles = "No triangle possible.";
} else {
var angleA_rad = Math.asin(ratio);
var angleA_deg_sol1 = radToDeg(angleA_rad);
var angleC_deg_sol1 = 180 – angleB_deg – angleA_deg_sol1;
var sideC_sol1 = (sideA * Math.sin(degToRad(angleC_deg_sol1))) / Math.sin(angleB_rad);
unknownAngles = "Angle A: " + angleA_deg_sol1.toFixed(2) + "°, ";
unknownAngles += "Angle C: " + angleC_deg_sol1.toFixed(2) + "°, ";
unknownSides = "Side C: " + sideC_sol1.toFixed(2);
// Check for a second possible triangle
var angleA_deg_sol2 = 180 – angleA_deg_sol1;
if (angleA_deg_sol2 > 0 && angleB_deg + angleA_deg_sol2 < 180) {
var angleC_deg_sol2 = 180 – angleB_deg – angleA_deg_sol2;
var sideC_sol2 = (sideA * Math.sin(degToRad(angleC_deg_sol2))) / Math.sin(angleB_rad);
unknownAngles += "Ambiguous Case Solution 2: Angle A: " + angleA_deg_sol2.toFixed(2) + "°, ";
unknownAngles += "Angle C: " + angleC_deg_sol2.toFixed(2) + "°, ";
unknownSides += "Side C: " + sideC_sol2.toFixed(2);
}
}
}
}
// Display results
document.getElementById("area").innerHTML = area || "Area: Input sufficient values (e.g., 3 sides, or 2 sides and included angle) to calculate.";
document.getElementById("perimeter").innerHTML = perimeter || "Perimeter: Input 3 side lengths to calculate.";
document.getElementById("unknownSides").innerHTML = unknownSides ? "Unknown Sides: " + unknownSides : "";
document.getElementById("unknownAngles").innerHTML = unknownAngles ? "Unknown Angles: " + unknownAngles : "";
}
.calculator-wrapper {
font-family: sans-serif;
max-width: 600px;
margin: 20px auto;
padding: 20px;
border: 1px solid #ccc;
border-radius: 8px;
background-color: #f9f9f9;
}
.calculator-wrapper h2 {
text-align: center;
color: #333;
margin-bottom: 15px;
}
.calculator-wrapper p {
color: #555;
line-height: 1.6;
margin-bottom: 20px;
}
.input-section {
display: grid;
grid-template-columns: repeat(2, 1fr);
gap: 15px;
margin-bottom: 20px;
}
.input-section label {
display: block;
margin-bottom: 5px;
font-weight: bold;
color: #333;
}
.input-section input[type="number"] {
width: calc(100% – 12px);
padding: 8px;
border: 1px solid #ccc;
border-radius: 4px;
box-sizing: border-box;
}
.calculator-wrapper button {
display: block;
width: 100%;
padding: 10px 15px;
background-color: #007bff;
color: white;
border: none;
border-radius: 5px;
cursor: pointer;
font-size: 16px;
margin-bottom: 20px;
}
.calculator-wrapper button:hover {
background-color: #0056b3;
}
#result {
background-color: #e9ecef;
padding: 15px;
border-radius: 5px;
border: 1px solid #ced4da;
}
#result h3 {
margin-top: 0;
color: #333;
border-bottom: 1px solid #ccc;
padding-bottom: 5px;
margin-bottom: 10px;
}
#result p {
margin-bottom: 8px;
color: #495057;
}
#result p:last-child {
margin-bottom: 0;
}