What's the difference between a leg and the hypotenuse?

The two legs are the sides that form the 90-degree angle. The hypotenuse is the longest side, opposite the right angle. In a 5-12-13 triangle, 5 and 12 are legs; 13 is the hypotenuse.

Why do the two acute angles always add to 90 degrees?

Because all angles in any triangle sum to 180°. Since one angle is already 90°, the remaining two must total 90°. This is why they're called complementary angles.

Can I use this for isosceles right triangles?

Yes. If both legs are equal (e.g., 5 and 5), the calculator will show a hypotenuse of 5√2 ≈ 7.07, and both acute angles will be exactly 45°.

What if I only know the hypotenuse and one leg?

This calculator requires both legs as input. If you know the hypotenuse and one leg, use the rearranged Pythagorean theorem: missing leg = √(hypotenuse² − known leg²).

Are there famous right triangles I should know?

Yes. The 3-4-5, 5-12-13, and 8-15-17 triangles are Pythagorean triples (all sides are whole numbers). The 45-45-90 and 30-60-90 triangles have standard angle ratios used in trigonometry.

How accurate are the angle calculations?

The calculator uses standard inverse trigonometric functions and typically displays results to 2 decimal places. For most practical purposes, this precision is sufficient.

Right Triangle Calculator

What this calculator does

A right triangle has one 90-degree angle and two legs that meet at that angle. This calculator takes the lengths of those two legs and instantly computes three key properties: the hypotenuse (the longest side), the total area, and the two non-right angles.

How it works

When you enter the lengths of leg a and leg b, the calculator applies three fundamental geometric relationships:

Hypotenuse: Uses the Pythagorean theorem to find the side opposite the right angle.
Area: Multiplies the two legs and divides by 2 (since a right triangle is half a rectangle).
Angles: Uses inverse trigonometric functions to find the two acute angles, which always sum to 90°.

All three results are computed instantly and can be used to verify triangle properties or solve real-world problems in construction, navigation, or design.

The formula

c = √(a² + b²) — and Area = (a × b) / 2 — and angle A = arctan(a / b)

Where c is the hypotenuse, a and b are the two legs, and the angles are measured in degrees.

Worked example

Suppose you have a right triangle with leg a = 5 units and leg b = 12 units.

Step 1: Calculate the hypotenuse

c = √(5² + 12²)
c = √(25 + 144)
c = √169
c = 13 units

Step 2: Calculate the area

Area = (5 × 12) / 2
Area = 60 / 2
Area = 30 square units

Step 3: Calculate the angles

The angle opposite leg a = arctan(5 / 12) ≈ 22.62°
The angle opposite leg b = arctan(12 / 5) ≈ 67.38°
Check: 22.62° + 67.38° + 90° = 180° ✓

This is the famous 5-12-13 Pythagorean triple, commonly used in construction and geometry problems.

Practical uses

Right triangle calculations appear frequently in real situations:

Ladders and walls: If a ladder is 13 feet long and leans against a wall 5 feet away, how high does it reach? Answer: 12 feet.
Roof pitch: Carpenters use right triangles to calculate roof angles and material lengths.
Land surveying: Surveyors use right triangles to measure distances and angles across terrain.
Screen diagonals: A TV advertised as 55 inches refers to the hypotenuse of the screen's rectangular shape.

Things to watch

Always enter positive numbers. The calculator expects both legs to be greater than zero; negative or zero values won't produce meaningful results.

Units must match. If leg a is in meters, leg b must also be in meters. The output will use the same unit.

The hypotenuse is always longest. Because of the Pythagorean theorem, the hypotenuse will always be longer than either individual leg. If your result shows otherwise, double-check your inputs.

Angles are in degrees. The calculator returns angles as decimal degrees (e.g., 22.62°), not degrees-minutes-seconds or radians. If you need a different format, multiply by π/180 to convert to radians.

Rounding in real-world projects. In construction or engineering, small rounding differences matter. If you're building something physical, use all decimal places during calculations and round only the final measurement.