What input combinations does the Triangle Calculator accept?

Any three of the six values: three sides (SSS), two sides and the angle between them (SAS), two angles and any side (ASA or AAS), or two sides and a non-included angle (SSA).

How does the Triangle Calculator find the missing angles?

It uses the law of cosines (c² = a² + b² − 2ab·cos C) when three sides or two sides and an included angle are known, and the law of sines (a / sin A = b / sin B = c / sin C) when two angles are known.

How is the triangle's area calculated?

Once all three sides are known, the Triangle Calculator uses Heron's formula: area = √(s(s−a)(s−b)(s−c)), where s is the semi-perimeter (a+b+c)/2.

Why does the Triangle Calculator sometimes show an error for SSA input?

Two sides and a non-included angle is the classic ambiguous case in trigonometry — depending on the numbers there may be zero, one, or two valid triangles. The calculator reports an error when no triangle can close.

What does the triangle type label mean?

It combines an angle classification (right, acute, or obtuse) with a side classification (scalene, isosceles, or equilateral) — for example 'Right scalene triangle' for a 3-4-5 triangle.

Does the Triangle Calculator upload my measurements?

No. All the trigonometry runs locally in your browser. The values you type into the Triangle Calculator never leave your device.

Triangle Calculator Online

Solve a triangle from any three known sides or angles and get every side, angle, area, and perimeter. Everything runs in your browser.

The Triangle Calculator runs entirely in your browser. The side lengths and angles you enter are computed locally and are never uploaded to ArrayKit.

Open the Right Triangle Calculator

About Triangle Calculator

The Triangle Calculator solves any triangle from three known measurements — three sides (SSS), two sides and the included angle (SAS), two angles and a side (ASA or AAS), or two sides and a non-included angle (SSA). Enter any three of the six values (sides a, b, c and angles A, B, C) and it fills in the rest using the law of cosines and the law of sines, then reports the area, perimeter, and whether the triangle is right, acute, obtuse, scalene, isosceles, or equilateral. It is useful for geometry homework, construction and layout measurements, surveying, and any time you know part of a triangle and need the rest. Built for students, engineers, and hobbyists who want an instant answer without doing trigonometry by hand. Every calculation happens locally — no measurements are uploaded.

Features

Solve a triangle from any three of its six sides and angles
Handles SSS, SAS, ASA, AAS, and SSA input combinations
Uses the law of cosines and law of sines for exact solutions
Reports area (Heron's formula), perimeter, and all missing sides/angles
Classifies the triangle as right, acute, or obtuse
Classifies the triangle as scalene, isosceles, or equilateral
Flags impossible inputs, like sides that fail the triangle inequality
Copy a plain-text summary of every result with one click
Runs entirely in your browser with no measurements sent anywhere

How to use the Triangle Calculator

Enter any three known values across the six side and angle fields
Leave the other three fields blank so the calculator knows what to solve
Review the solved sides, angles, area, perimeter, and triangle type
Copy the result summary if you need to paste it elsewhere

Example

Input

a=3, b=4, c=5

Output

Right triangle · area 6

A classic 3-4-5 right triangle: the law of cosines confirms angle C is 90°.

Common errors & troubleshooting

The calculator says the side lengths cannot form a triangle. — Each side must be shorter than the sum of the other two (the triangle inequality). Double-check for a typo, like a missing decimal point.
Result shows an error for two sides and a non-included angle (SSA). — SSA is the ambiguous case — with these values no triangle closes, or the angle is too large for the shorter given side. Try increasing the side opposite the angle.
Nothing solves after entering values. — Make sure exactly three of the six fields are filled in — fewer than three is underdetermined, and more than three can conflict with each other.
Angles entered as SSS by mistake. — The three angle fields (A, B, C) are separate from the three side fields (a, b, c) — mixing them up gives an unsolvable or nonsensical combination.

Frequently asked questions

What input combinations does the Triangle Calculator accept?: Any three of the six values: three sides (SSS), two sides and the angle between them (SAS), two angles and any side (ASA or AAS), or two sides and a non-included angle (SSA).
How does the Triangle Calculator find the missing angles?: It uses the law of cosines (c² = a² + b² − 2ab·cos C) when three sides or two sides and an included angle are known, and the law of sines (a / sin A = b / sin B = c / sin C) when two angles are known.
How is the triangle's area calculated?: Once all three sides are known, the Triangle Calculator uses Heron's formula: area = √(s(s−a)(s−b)(s−c)), where s is the semi-perimeter (a+b+c)/2.
Why does the Triangle Calculator sometimes show an error for SSA input?: Two sides and a non-included angle is the classic ambiguous case in trigonometry — depending on the numbers there may be zero, one, or two valid triangles. The calculator reports an error when no triangle can close.
What does the triangle type label mean?: It combines an angle classification (right, acute, or obtuse) with a side classification (scalene, isosceles, or equilateral) — for example 'Right scalene triangle' for a 3-4-5 triangle.
Does the Triangle Calculator upload my measurements?: No. All the trigonometry runs locally in your browser. The values you type into the Triangle Calculator never leave your device.

Related tools

Right Triangle Calculator — Solve a right triangle from any two sides or a side and an angle.
Pythagorean Theorem Calculator — Find a missing side of a right triangle with a²+b²=c².
Area Calculator — Calculate the area of circles, rectangles, triangles, trapezoids and more.
Circle Calculator — Find a circle’s radius, diameter, circumference and area from any one value.
Slope Calculator — Find the slope, intercept, distance and equation of a line through two points.
Surface Area Calculator — Calculate the surface area of spheres, cylinders, cones, boxes and more.