Enter any two sides of a right triangle to find the missing side. The calculator solves for the hypotenuse or either leg and shows each step of the working.
Leave the side you want to find blank. Use any consistent unit (cm, m, ft, in).
a2 + b2 = c2, where a and b are the two legs and c is the hypotenuse of a right triangle.
The hypotenuse is always opposite the right angle and is the longest side. Rearranging the formula lets you solve for any side:
The 3-4-5 triangle is the most common Pythagorean triple. Here is how to confirm it from scratch.
A right triangle with legs 3 and 4 always has a hypotenuse of 5, no matter the unit. Scale it up: a = 6, b = 8 gives c = 10.
For the history and proof of the theorem, see Wolfram MathWorld on the Pythagorean theorem.
Pythagorean triples are sets of whole numbers that satisfy a^2 + b^2 = c^2. The most useful ones to memorize:
| a | b | c |
|---|---|---|
| 3 | 4 | 5 |
| 5 | 12 | 13 |
| 8 | 15 | 17 |
| 7 | 24 | 25 |
Find the slope of a line, solve a quadratic, or compute a square root.
Square both known sides, then add or subtract. To find the hypotenuse c, use c = sqrt(a^2 + b^2). To find a missing leg a, use a = sqrt(c^2 - b^2). The calculator handles all three cases automatically.
The formula is a^2 + b^2 = c^2, where a and b are the two shorter sides (legs) of a right triangle, and c is the longest side (hypotenuse) opposite the right angle.
Yes. Enter any two sides and this calculator solves for the third. It shows the substituted formula and each arithmetic step so you can follow the working.
If you know the hypotenuse c and one leg b, the missing leg a = sqrt(c^2 - b^2). For example, with c = 13 and b = 5: a = sqrt(169 - 25) = sqrt(144) = 12.
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