Right Triangle Calculator

Enter any two known values to solve the entire right triangle.

This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.

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How to Use the Right Triangle Calculator

This calculator solves any right triangle when you provide two known values. It accepts both side lengths and angle measurements.

  1. Enter two known values. Fill in any combination of two values: two sides, one side and one angle, or the hypotenuse and one angle. Leave all other fields empty.
  2. Read the full solution. The calculator finds all three sides, both acute angles, the area, and the perimeter. Results update instantly.
  3. Copy or share. Use the action buttons to copy the solution or generate a shareable link.

Valid input combinations include: two legs, one leg and hypotenuse, one leg and one acute angle, or the hypotenuse and one acute angle. Entering two angles without a side is not enough to determine the triangle's size. The right angle (C = 90 degrees) is assumed and does not need to be entered.

About Right Triangle Geometry

A right triangle has one 90-degree angle. The side opposite the right angle is the hypotenuse, always the longest side. The other two sides are called legs. The two acute angles always sum to 90 degrees. Right triangles are fundamental in trigonometry, where the ratios of the sides define the sine, cosine, and tangent functions. They appear constantly in construction (checking if corners are square), navigation (finding distances), physics (resolving forces into components), and computer graphics (calculating distances and angles). The Pythagorean theorem (a^2 + b^2 = c^2) governs the relationship between the sides.

Frequently Asked Questions

What inputs do I need to solve a right triangle?

You need exactly two values, and at least one must be a side length. Valid combinations: two sides, one side plus one acute angle. Two angles alone cannot determine the size of the triangle.

How are the angles calculated from the sides?

When two sides are known, the angles are found using inverse trigonometric functions. For example, angle A = arctan(a/b), or A = arcsin(a/c). The other acute angle is then 90 minus A.

What is the difference between this and the Pythagorean Theorem calculator?

The Pythagorean Theorem calculator only finds a missing side from two known sides. This Right Triangle calculator is more complete: it also handles angle inputs and outputs the area, perimeter, and all angles in addition to the sides.