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Right Triangle Calculator

Solve a right triangle from any two known values.

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How it was solved

Full solution

ElementValue

SOH-CAH-TOA

Sine = opposite ÷ hypotenuse. Cosine = adjacent ÷ hypotenuse. Tangent = opposite ÷ adjacent. Those three relationships cover every question a right triangle can pose, and the inverse functions turn side ratios back into angles.

Hypotenuse

—

Sides and angles

Leg a—
Leg b—
Angle A—
Angle B—

Measures

Area—
Perimeter—

—

The two acute angles always sum to 90°

Two values are always enough to solve a right triangle, as long as at least one is a side — the right angle supplies the third piece of information. Angles are in degrees, and sides in whatever unit you enter.

Quick Tool Overview

The Right Triangle Calculator solves a triangle completely from any two known values — two sides, or a side and an acute angle — reporting every remaining side and angle plus area, perimeter, altitude, inradius and circumradius.

What it does
Solves a right triangle from any two known values
You give it
Two sides, or one side and one acute angle
You get back
All sides and angles plus area and perimeter
Best for
Trigonometry coursework, surveying and construction
Calculators Free, unlimited use No sign-up Runs in your browser

About the Right Triangle Calculator

Solve a right triangle completely from any two known values: two sides, or one side and one acute angle. Every remaining side and angle is calculated, along with the area, perimeter, altitude to the hypotenuse, inradius and circumradius.

Two known values are always enough, because the right angle itself counts as the third piece of information — which is what makes right triangles so much easier to solve than general ones. The relationships come from SOH-CAH-TOA, and the calculator prints which one it used for each step. The two acute angles always sum to 90 degrees, so finding one immediately gives the other.

Key features of the Right Triangle Calculator

Any two values are enough

The right angle supplies the third piece of information, which is what makes these triangles solvable so easily.

Shows which rule it used

Each step names the SOH-CAH-TOA relationship applied, so the working can be reproduced.

Angle or side entry

Enter two sides, or a side and an angle — both routes solve the triangle completely.

Derived values included

Altitude to the hypotenuse, inradius and circumradius, which follow-up questions tend to ask for.

Validates the input

Impossible combinations are refused with an explanation rather than producing a nonsense triangle.

How to use the Right Triangle Calculator

  1. 1

    Choose what you know

    Two sides, or one side and one acute angle.

  2. 2

    Enter the values

    Sides in any consistent unit; angles in degrees.

  3. 3

    Read the solution

    Every side and angle, with the trigonometric relationship used for each shown.

  4. 4

    Check the derived values

    Area, perimeter, altitude, inradius and circumradius are calculated too.

Frequently asked questions

Two, as long as at least one is a side. The right angle supplies the third piece of information, which is why right triangles need less than general triangles do.

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