Enter two sides and one angle, or one side and two angles, to calculate the missing angles of a triangle.
Enter at least three values.
Understanding the Triangle Angle Calculator
This calculator helps determine the unknown angles of a triangle when you have sufficient information. A triangle has three sides and three interior angles. The sum of the interior angles of any triangle is always 180 degrees.
To uniquely define a triangle, you typically need at least three pieces of information, with at least one being a side length. This calculator supports solving for missing angles based on the following common triangle congruence postulates:
Side-Side-Side (SSS): If all three sides are known, you can find all three angles using the Law of Cosines.
Side-Angle-Side (SAS): If two sides and the included angle are known, you can find the third side using the Law of Cosines, and then use the Law of Sines or Cosines to find the remaining angles.
Angle-Side-Angle (ASA): If two angles and the included side are known, you can find the third angle (since the sum is 180°), and then use the Law of Sines to find the lengths of the other two sides.
Angle-Angle-Side (AAS): If two angles and a non-included side are known, you can find the third angle, and then use the Law of Sines to find the remaining sides.
Important Note: When using the Law of Sines to find angles, there can sometimes be an "ambiguous case" (SSA) where two different triangles might be possible. This calculator assumes standard triangle properties and aims to provide a single, valid solution where possible. For SSA scenarios, ensure the input logically leads to a single triangle.
Mathematical Formulas Used:
Sum of Angles: Angle A + Angle B + Angle C = 180°
Law of Cosines: a² = b² + c² – 2bc * cos(A) => cos(A) = (b² + c² – a²) / (2bc) b² = a² + c² – 2ac * cos(B) => cos(B) = (a² + c² – b²) / (2ac) c² = a² + b² – 2ab * cos(C) => cos(C) = (a² + b² – c²) / (2ab)
(Where a, b, c are side lengths opposite angles A, B, C respectively)
Law of Sines: a / sin(A) = b / sin(B) = c / sin(C)
How to Use:
Fill in at least three of the input fields (sides or angles). The calculator will attempt to solve for the missing angles based on the provided information. Ensure units are consistent (e.g., all side lengths in cm or inches, angles in degrees).
Example: If you know Side A = 10, Side B = 12, and Angle C = 60°, the calculator can find Angle A and Angle B.
function calculateTriangleAngles() {
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 resultDiv = document.getElementById("result");
var errorDiv = document.getElementById("errorMessage");
errorDiv.innerText = ""; // Clear previous errors
var knownValues = 0;
var inputs = [sideA, sideB, sideC, angleA_deg, angleB_deg, angleC_deg];
for (var i = 0; i 0) {
knownValues++;
}
}
if (knownValues = 3 && !isNaN(sideA) && !isNaN(sideB) && !isNaN(sideC)) {
if (sideA + sideB <= sideC || sideA + sideC <= sideB || sideB + sideC <= sideA) {
potentialErrors.push("Invalid triangle: Side lengths do not satisfy the triangle inequality.");
} else {
calculatedAngles.angleA = Math.acos((sideB * sideB + sideC * sideC – sideA * sideA) / (2 * sideB * sideC)) * 180 / Math.PI;
calculatedAngles.angleB = Math.acos((sideA * sideA + sideC * sideC – sideB * sideB) / (2 * sideA * sideC)) * 180 / Math.PI;
calculatedAngles.angleC = 180 – calculatedAngles.angleA – calculatedAngles.angleB;
// Update UI if angles were missing
if (isNaN(angleA_deg)) document.getElementById("angleA").value = calculatedAngles.angleA.toFixed(2);
if (isNaN(angleB_deg)) document.getElementById("angleB").value = calculatedAngles.angleB.toFixed(2);
if (isNaN(angleC_deg)) document.getElementById("angleC").value = calculatedAngles.angleC.toFixed(2);
}
}
// Case 2: SAS (Two sides and included angle known)
if (!isNaN(angleC_deg) && !isNaN(sideA) && !isNaN(sideB)) {
// Calculate side c using Law of Cosines
var c_squared = sideA * sideA + sideB * sideB – 2 * sideA * sideB * Math.cos(angleC_rad);
if (c_squared = -1 && cosA <= 1) {
calculatedAngles.angleA = Math.acos(cosA) * 180 / Math.PI;
if (isNaN(angleA_deg)) document.getElementById("angleA").value = calculatedAngles.angleA.toFixed(2);
} else {
potentialErrors.push("Invalid input for SAS (cos(A) out of range).");
}
calculatedAngles.angleB = 180 – calculatedAngles.angleA – angleC_deg;
if (isNaN(angleB_deg)) document.getElementById("angleB").value = calculatedAngles.angleB.toFixed(2);
}
}
if (!isNaN(angleB_deg) && !isNaN(sideA) && !isNaN(sideC)) {
var b_squared = sideA * sideA + sideC * sideC – 2 * sideA * sideC * Math.cos(angleB_rad);
if (b_squared = -1 && cosA <= 1) {
calculatedAngles.angleA = Math.acos(cosA) * 180 / Math.PI;
if (isNaN(angleA_deg)) document.getElementById("angleA").value = calculatedAngles.angleA.toFixed(2);
} else {
potentialErrors.push("Invalid input for SAS (cos(A) out of range).");
}
calculatedAngles.angleC = 180 – calculatedAngles.angleA – angleB_deg;
if (isNaN(angleC_deg)) document.getElementById("angleC").value = calculatedAngles.angleC.toFixed(2);
}
}
if (!isNaN(angleA_deg) && !isNaN(sideB) && !isNaN(sideC)) {
var a_squared = sideB * sideB + sideC * sideC – 2 * sideB * sideC * Math.cos(angleA_rad);
if (a_squared = -1 && cosB <= 1) {
calculatedAngles.angleB = Math.acos(cosB) * 180 / Math.PI;
if (isNaN(angleB_deg)) document.getElementById("angleB").value = calculatedAngles.angleB.toFixed(2);
} else {
potentialErrors.push("Invalid input for SAS (cos(B) out of range).");
}
calculatedAngles.angleC = 180 – angleA_deg – calculatedAngles.angleB;
if (isNaN(angleC_deg)) document.getElementById("angleC").value = calculatedAngles.angleC.toFixed(2);
}
}
// Case 3: ASA/AAS (Two angles and a side known)
// First, calculate the third angle if two are known
var calculatedThirdAngle = NaN;
if (!isNaN(angleA_deg) && !isNaN(angleB_deg) && isNaN(angleC_deg)) {
calculatedThirdAngle = 180 – angleA_deg – angleB_deg;
if (calculatedThirdAngle <= 0) potentialErrors.push("Invalid triangle: Sum of two angles exceeds 180 degrees.");
else {
calculatedAngles.angleC = calculatedThirdAngle;
document.getElementById("angleC").value = calculatedAngles.angleC.toFixed(2);
}
} else if (!isNaN(angleA_deg) && !isNaN(angleC_deg) && isNaN(angleB_deg)) {
calculatedThirdAngle = 180 – angleA_deg – angleC_deg;
if (calculatedThirdAngle <= 0) potentialErrors.push("Invalid triangle: Sum of two angles exceeds 180 degrees.");
else {
calculatedAngles.angleB = calculatedThirdAngle;
document.getElementById("angleB").value = calculatedAngles.angleB.toFixed(2);
}
} else if (!isNaN(angleB_deg) && !isNaN(angleC_deg) && isNaN(angleA_deg)) {
calculatedThirdAngle = 180 – angleB_deg – angleC_deg;
if (calculatedThirdAngle 0) { // If we just calculated a third angle
if (!isNaN(sideA) && isNaN(sideB)) { needsSideCalc = true; var knownSide = sideA; var knownAngle = calculatedAngles.angleA; var targetAngle = calculatedAngles.angleB; var targetSide = 'sideB'; }
else if (!isNaN(sideA) && isNaN(sideC)) { needsSideCalc = true; var knownSide = sideA; var knownAngle = calculatedAngles.angleA; var targetAngle = calculatedAngles.angleC; var targetSide = 'sideC'; }
else if (!isNaN(sideB) && isNaN(sideA)) { needsSideCalc = true; var knownSide = sideB; var knownAngle = calculatedAngles.angleB; var targetAngle = calculatedAngles.angleA; var targetSide = 'sideA'; }
else if (!isNaN(sideB) && isNaN(sideC)) { needsSideCalc = true; var knownSide = sideB; var knownAngle = calculatedAngles.angleB; var targetAngle = calculatedAngles.angleC; var targetSide = 'sideC'; }
else if (!isNaN(sideC) && isNaN(sideA)) { needsSideCalc = true; var knownSide = sideC; var knownAngle = calculatedAngles.angleC; var targetAngle = calculatedAngles.angleA; var targetSide = 'sideA'; }
else if (!isNaN(sideC) && isNaN(sideB)) { needsSideCalc = true; var knownSide = sideC; var knownAngle = calculatedAngles.angleC; var targetAngle = calculatedAngles.angleB; var targetSide = 'sideB'; }
if (needsSideCalc && !isNaN(knownSide) && !isNaN(knownAngle) && !isNaN(targetAngle)) {
var calculatedSideVal = (knownSide * Math.sin(targetAngle * Math.PI / 180)) / Math.sin(knownAngle * Math.PI / 180);
calculatedSides[targetSide] = calculatedSideVal;
if (!isNaN(calculatedSideVal)) {
document.getElementById(targetSide).value = calculatedSideVal.toFixed(2);
} else {
potentialErrors.push("Error calculating side using Law of Sines.");
}
}
}
// If we still have unknown angles but calculated sides, try Law of Cosines/Sines again
var currentKnownAngles = [
!isNaN(calculatedAngles.angleA) ? calculatedAngles.angleA : NaN,
!isNaN(calculatedAngles.angleB) ? calculatedAngles.angleB : NaN,
!isNaN(calculatedAngles.angleC) ? calculatedAngles.angleC : NaN
];
var currentKnownSides = [
!isNaN(calculatedSides.sideA) ? calculatedSides.sideA : NaN,
!isNaN(calculatedSides.sideB) ? calculatedSides.sideB : NaN,
!isNaN(calculatedSides.sideC) ? calculatedSides.sideC : NaN
];
// Recalculate if possible after initial pass
var anglesUpdated = false;
var sidesUpdated = false;
// Try Law of Sines if we have 2 angles and 1 side
if (currentKnownAngles.filter(a => !isNaN(a)).length >= 2 && currentKnownSides.filter(s => !isNaN(s)).length >= 1) {
var a = currentKnownSides[0], b = currentKnownSides[1], c = currentKnownSides[2];
var A = currentKnownAngles[0], B = currentKnownAngles[1], C = currentKnownAngles[2];
if (isNaN(A) && !isNaN(a) && !isNaN(B) && !isNaN(C)) { A = 180 – B – C; if (A <= 0) potentialErrors.push("Invalid triangle (angle A calc)."); else { calculatedAngles.angleA = A; anglesUpdated = true; } }
if (isNaN(B) && !isNaN(b) && !isNaN(A) && !isNaN(C)) { B = 180 – A – C; if (B <= 0) potentialErrors.push("Invalid triangle (angle B calc)."); else { calculatedAngles.angleB = B; anglesUpdated = true; } }
if (isNaN(C) && !isNaN(c) && !isNaN(A) && !isNaN(B)) { C = 180 – A – B; if (C !isNaN(s)).length === 3 && currentKnownAngles.filter(a => !isNaN(a)).length = -1 && cosA_val = -1 && cosB_val = -1 && cosC_val 0.1) { // Allow for small floating point inaccuracies
potentialErrors.push("Calculated angles do not sum to 180 degrees. Check your inputs.");
}
}
// Display Results
if (potentialErrors.length > 0) {
errorDiv.innerText = "Error: " + potentialErrors.join(" ");
resultDiv.innerText = "Calculation failed.";
resultDiv.style.backgroundColor = "#dc3545"; // Red for error
} else {
resultDiv.innerText = "Angles: A=" + calculatedAngles.angleA.toFixed(2) + "°, B=" + calculatedAngles.angleB.toFixed(2) + "°, C=" + calculatedAngles.angleC.toFixed(2) + "°";
resultDiv.style.backgroundColor = "#28a745"; // Success Green
}
}
function clearInputs() {
document.getElementById("sideA").value = "";
document.getElementById("sideB").value = "";
document.getElementById("sideC").value = "";
document.getElementById("angleA").value = "";
document.getElementById("angleB").value = "";
document.getElementById("angleC").value = "";
document.getElementById("result").innerText = "Enter at least three values.";
document.getElementById("result").style.backgroundColor = "#ddd"; // Reset to default-like
document.getElementById("errorMessage").innerText = "";
}