Calculate various properties of a triangle by providing at least three pieces of information. This calculator can determine area, perimeter, and missing side lengths or angles based on the inputs.
Please enter at least three values to calculate.
Understanding Triangle Calculations
Triangles are fundamental geometric shapes with three sides and three angles. The sum of the interior angles of any triangle is always 180 degrees. Calculating properties of triangles is crucial in fields like engineering, architecture, navigation, and physics.
Key Triangle Properties and Formulas:
Perimeter: The total length of all sides. For a triangle with sides A, B, and C, the perimeter (P) is calculated as: P = A + B + C
Area: The space enclosed by the triangle. Several formulas exist depending on the available information:
Base and Height: If you know the base (b) and the perpendicular height (h) to that base: Area = 0.5 * b * h
Heron's Formula (when all three sides are known): First, calculate the semi-perimeter (s): s = (A + B + C) / 2. Then, the area (K) is: K = sqrt(s * (s - A) * (s - B) * (s - C))
Two Sides and Included Angle (SAS): If you know sides A and B, and the angle C between them: Area = 0.5 * A * B * sin(C) (Note: Angle C must be in radians for most programming functions, or converted from degrees).
Two Angles and Included Side (ASA) / AAS: These cases typically involve using the Law of Sines to find missing sides or angles first.
Angles: As mentioned, Angle A + Angle B + Angle C = 180°.
Law of Sines: Relates the lengths of sides of a triangle to the sines of its opposite angles. A/sin(A) = B/sin(B) = C/sin(C). Useful for ASA, AAS, SSA cases.
Law of Cosines: Relates the lengths of the sides of a triangle to the cosine of one of its angles.
A² = B² + C² - 2*B*C*cos(A)
B² = A² + C² - 2*A*C*cos(B)
C² = A² + B² - 2*A*B*cos(C)
Useful for SAS, SSS cases.
Use Cases for Triangle Calculators:
Construction & Architecture: Calculating roof pitches, beam lengths, and structural stability.
Navigation: Determining distances and bearings using triangulation.
Surveying: Mapping land boundaries and calculating areas.
Physics: Analyzing forces and vectors in equilibrium or motion.
Computer Graphics: Rendering 3D models and manipulating polygons.
Everyday Problems: Estimating distances or heights when direct measurement is difficult.
This calculator attempts to derive as many properties as possible based on the input provided, accommodating various common triangle calculation scenarios.
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 resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
var inputs = [sideA, sideB, sideC, angleA_deg, angleB_deg, angleC_deg].filter(val => !isNaN(val));
var numSidesKnown = [!isNaN(sideA), !isNaN(sideB), !isNaN(sideC)].filter(Boolean).length;
var numAnglesKnown = [!isNaN(angleA_deg), !isNaN(angleB_deg), !isNaN(angleC_deg)].filter(Boolean).length;
if (inputs.length calculatedSideC &&
calculatedSideA + calculatedSideC > calculatedSideB &&
calculatedSideB + calculatedSideC > calculatedSideA) {
perimeter = calculatePerimeter();
area = calculateAreaHeron();
if (isNaN(calculatedAngleA) || isNaN(calculatedAngleB) || isNaN(calculatedAngleC)) {
// Use Law of Cosines to find angles if not provided
if (isNaN(calculatedAngleA)) {
var cosA = (calculatedSideB*calculatedSideB + calculatedSideC*calculatedSideC – calculatedSideA*calculatedSideA) / (2 * calculatedSideB * calculatedSideC);
if (cosA >= -1 && cosA = -1 && cosB = -1 && cosC 1 || sinB_val 0) { // First solution is valid
// If sideC was not provided, calculate it for the first solution
if (isNaN(calculatedSideC)) {
var tempSideC1 = (calculatedSideA * Math.sin(degreesToRadians(angleC1))) / Math.sin(degreesToRadians(calculatedAngleA));
// Store this potential solution if it's the first valid one found
if (isNaN(calculatedSideC)) { // Only update if side C wasn't already calculated via other means
calculatedSideC = tempSideC1;
calculatedAngleB = angleB1;
calculatedAngleC = angleC1;
perimeter = calculatePerimeter();
area = calculateAreaSAS(calculatedSideA, calculatedSideB, calculatedAngleC);
}
}
}
if (angleC2 > 0 && angleB2 !== angleB1) { // Second solution is valid and distinct
// This calculator will not explicitly display both solutions for SSA.
// It will use the first valid solution found or prefer a definite calculation.
// For a full SSA calculator, display logic would need to be more complex.
// We ensure angleB and angleC are updated if a valid second solution exists and wasn't overwritten.
if (isNaN(calculatedSideC)) { // Only update if side C wasn't already calculated
var tempSideC2 = (calculatedSideA * Math.sin(degreesToRadians(angleC2))) / Math.sin(degreesToRadians(calculatedAngleA));
// If side C is still NaN, and angleB/C were not set by a prior valid calculation, update them.
if (isNaN(calculatedSideC)) {
calculatedSideC = tempSideC2;
calculatedAngleB = angleB2; // Prefer the second angleB if angleC2 is valid
calculatedAngleC = angleC2;
perimeter = calculatePerimeter(); // Recalculate
area = calculateAreaSAS(calculatedSideA, calculatedSideB, calculatedAngleC); // Recalculate
}
}
}
}
}
// Handle other SSA permutations similarly if needed, prioritizing finding *a* solution.
}
// Final Check: If area or perimeter is still NaN, try to calculate if possible
if (isNaN(perimeter)) perimeter = calculatePerimeter();
if (isNaN(area)) area = calculateAreaHeron(); // Fallback to Heron if sides are known
if (isNaN(area)) { // Try SAS if applicable
if (!isNaN(calculatedSideA) && !isNaN(calculatedSideB) && !isNaN(calculatedAngleC)) area = calculateAreaSAS(calculatedSideA, calculatedSideB, calculatedAngleC);
else if (!isNaN(calculatedSideA) && !isNaN(calculatedSideC) && !isNaN(calculatedAngleB)) area = calculateAreaSAS(calculatedSideA, calculatedSideC, calculatedAngleB);
else if (!isNaN(calculatedSideB) && !isNaN(calculatedSideC) && !isNaN(calculatedAngleA)) area = calculateAreaSAS(calculatedSideB, calculatedSideC, calculatedAngleA);
}
// — Display Results —
var outputHTML = "
Calculated Properties:
";
outputHTML += "";
if (!isNaN(perimeter)) {
outputHTML += "Perimeter:" + perimeter.toFixed(4) + " units";
} else {
outputHTML += "Perimeter: Not enough information or invalid input.";
}
if (!isNaN(area)) {
outputHTML += "Area:" + area.toFixed(4) + " square units";
} else {
outputHTML += "Area: Not enough information or invalid input.";
}
if (!isNaN(calculatedSideA)) {
outputHTML += "Side A:" + calculatedSideA.toFixed(4) + " units";
} else {
outputHTML += "Side A: Not calculated";
}
if (!isNaN(calculatedSideB)) {
outputHTML += "Side B:" + calculatedSideB.toFixed(4) + " units";
} else {
outputHTML += "Side B: Not calculated";
}
if (!isNaN(calculatedSideC)) {
outputHTML += "Side C:" + calculatedSideC.toFixed(4) + " units";
} else {
outputHTML += "Side C: Not calculated";
}
if (!isNaN(calculatedAngleA)) {
outputHTML += "Angle A:" + calculatedAngleA.toFixed(4) + "°";
} else {
outputHTML += "Angle A: Not calculated";
}
if (!isNaN(calculatedAngleB)) {
outputHTML += "Angle B:" + calculatedAngleB.toFixed(4) + "°";
} else {
outputHTML += "Angle B: Not calculated";
}
if (!isNaN(calculatedAngleC)) {
outputHTML += "Angle C:" + calculatedAngleC.toFixed(4) + "°";
} else {
outputHTML += "Angle C: Not calculated";
}
outputHTML += "";
resultDiv.innerHTML = outputHTML;
}