Right Triangle Calculator - Sides, Angles & Trig Ratios

Solve a Right Triangle from Two Legs

This right triangle calculator solves a complete right triangle from just its two legs. Enter leg a and leg b, and it instantly returns all three sides, both acute angles, the area, the perimeter, the trigonometric ratios (sin, cos, tan) for angle A, plus the inradius and circumradius — each backed by a step-by-step solution and a visual diagram.

A right triangle has exactly one 90° angle. The side opposite it is the hypotenuse (the longest side), and the two sides forming the right angle are the legs.

What It Calculates

All Three Sides

The two legs you enter plus the hypotenuse found with the Pythagorean theorem.

Both Acute Angles

Angles A and B from inverse trigonometry — always adding up to 90°.

Area & More

Area, perimeter, sin/cos/tan, inradius, and circumradius in a single view.

Private by design: every calculation runs in your browser — nothing you type is uploaded to a server.

How to Solve a Right Triangle

1

Enter Leg a

Type the length of leg a, the side adjacent to angle B.

2

Enter Leg b

Type the length of leg b, the side adjacent to angle A.

3

Read the Results

View every value at once: the hypotenuse, both angles, area, and perimeter.

4

Check the Trig Ratios

See the sin, cos, and tan values for angle A computed from the side lengths.

5

Expand the Steps

Open Solution Steps to follow the detailed calculation with formulas.

Choose your display: pick mm, cm, m, in, or ft for the sides, and switch angles between degrees and radians.

Formulas Behind the Results

From two legs, the calculator applies these standard right-triangle relationships:

Quantity	Formula
Hypotenuse	c = √(a² + b²)
Angle A	A = arctan(a / b)
Angle B	B = 90° − A
Area	(1/2) × a × b
Perimeter	a + b + c
Circumradius (R)	c / 2

Trigonometric Ratios for Angle A

Ratio	Definition
sin(A)	opposite / hypotenuse
cos(A)	adjacent / hypotenuse
tan(A)	opposite / adjacent

The circumradius equals half the hypotenuse because, in a right triangle, the hypotenuse is the diameter of the circumscribed circle.

Features

Hypotenuse from Pythagoras

The third side is computed with the Pythagorean theorem from your two legs.

Both Acute Angles

Angles A and B are found with inverse trigonometry and always total 90°.

Sin, Cos & Tan

Trigonometric ratios for angle A displayed alongside the side lengths.

Area & Perimeter

The enclosed area and the total boundary length are calculated automatically.

Inradius & Circumradius

The radii of the inscribed and circumscribed circles are shown too.

Steps & Visual Preview

A worked solution with formulas plus a labelled triangle diagram.

Right Triangle Questions Answered

How do I find the missing side of a right triangle?

Enter the two legs and the calculator finds the hypotenuse with the Pythagorean theorem, c = √(a² + b²). It is the longest side and always sits opposite the 90° angle.

How do I find the angles of a right triangle?

The two acute angles come from inverse trigonometry: angle A = arctan(a / b), and angle B = 90° − A. The two acute angles are complementary, so they always add up to 90°.

What are sin, cos, and tan in a right triangle?

For angle A, sin(A) = opposite / hypotenuse, cos(A) = adjacent / hypotenuse, and tan(A) = opposite / adjacent. The calculator shows all three ratios next to the side lengths.

How is the area of a right triangle calculated?

Area = (1/2) × leg a × leg b. Because the two legs meet at the right angle, they act as the base and height, which keeps the calculation simple.

What is the circumradius of a right triangle?

The circumradius (R) equals half the hypotenuse: R = c / 2. This is because the hypotenuse is the diameter of the circle that passes through all three vertices.

Can I switch units and angle mode?

Yes. Side lengths can be shown in mm, cm, m, in, or ft, and angles can be displayed in degrees or radians. Change either setting and the results update instantly.