Triangle Calculator
Solve any triangle from three sides, two sides and an angle, or two angles and a side. Get area, perimeter, angles, heights, radii and medians.
Enter three side lengths to solve the triangle.
Last updated: January 2026
How this calculator is verified
Checked by True Calculator automated test suite on
- Formula verified against a published worked example in the automated test suite
- Edge cases (zero, negative, boundary and unit-mismatch inputs) covered by unit tests
The full verification method is on our how we verify page. Found an error? Tell us and we will re-check it.
When to Use This Calculator
A roof truss is built as a right triangle with legs of 3 and 4 units. Choosing three sides (SSS) and entering 3, 4 and 5 returns an area of 6 square units, a perimeter of 12 units, angles of roughly 36.87 and 53.13 degrees plus the right angle, and heights of 4, 3 and 2.4 units. The 3-4-5 triple is exact, so the inradius is 1 and the circumradius is 2.5. Switched to radians, the right angle displays as about 1.5708 rad.
How to Use This Calculator
- Step 1: Choose the calculation method: three sides, two sides and an included angle, or two angles and an included side.
- Step 2: Pick the angle unit, degrees or radians, before entering any angles.
- Step 3: Enter the side lengths and angle measures shown for that mode; sides and angles must be positive.
- Step 4: Read the area, perimeter, triangle type, all three angles and heights, plus the inradius, circumradius and medians.
Worked Example
A roof truss is built as a right triangle with legs of 3 and 4 units. Choosing three sides (SSS) and entering 3, 4 and 5 returns an area of 6 square units, a perimeter of 12 units, angles of roughly 36.87 and 53.13 degrees plus the right angle, and heights of 4, 3 and 2.4 units. The 3-4-5 triple is exact, so the inradius is 1 and the circumradius is 2.5. Switched to radians, the right angle displays as about 1.5708 rad.
Tips and Common Mistakes
- •Tip 1: With three sides, verify that the longest side is shorter than the sum of the other two, or the triangle cannot exist.
- •Tip 2: In degrees mode the three angles always sum to 180 degrees, which is a reliable check for data entry slips.
- •Tip 3: For two sides and an angle, make sure the angle sits between the two given sides, since the wrong pair produces a different triangle.
- ✗Mistake 1: Entering three sides that violate the triangle inequality, such as 2, 3 and 6, for which no triangle exists.
- ✗Mistake 2: Mixing degrees and radians in one calculation — pick one unit and stick to it.
Frequently Asked Questions
What is the SSS method?
SSS (Side-Side-Side) uses all three sides. The calculator uses law of cosines for angles and Heron's formula for area.
What is the SAS method?
SAS (Side-Angle-Side) uses two sides and the included angle. The law of cosines finds the third side.
How is triangle area calculated?
From three sides: Heron's formula. From two sides and angle: ½ × a × b × sin(C).
What is the sine rule?
For any triangle, the ratio of each side to the sine of its opposite angle is equal: a/sin A = b/sin B = c/sin C. It is used to solve triangles when you know two angles and a side, or two sides and a non-included angle.
What is the cosine rule?
It relates the three sides to one angle: c² = a² + b² − 2ab·cos C. It is the tool for SAS triangles — two sides and the included angle — and for finding an angle when all three sides are known.
Compare these tools
- Percentage Calculator — Calculate percentages, percentage difference and percentage change instantly
- Rounding Calculator — Round any number to the nearest value, or up and down, to any decimal places
- Standard Form Calculator — Convert numbers to and from standard form (scientific notation) with one click
You might also need
Related calculators from other categories
Health & Fitness
Body Surface Area Calculator
Calculate body surface area in m² with Mosteller, DuBois and Haycock formulas — used in medicine and dosage calculations.
Science & Weather
Ideal Gas Law Calculator
Solve PV = nRT for pressure, volume, moles or temperature with the gas constant R = 8.314. Enter any three to find the fourth.
Construction
Roofing Calculator
Estimate roofing material, sloped roof area and cost from house footprint, roof pitch and waste allowance.
Construction
Square Footage Calculator
Calculate area of rectangles, triangles, circles, trapezoids and more in sq ft, metres and yards, with quantity and cost estimates.