Right Triangle Calculator
Hypotenuse, area, perimeter and both acute angles of a right triangle from its two legs, with the Pythagorean step shown before the square root.
With leg a 3 ft, leg b 4 ft, right triangle comes to 5.000 ft — hypotenuse. It is reached in 6 steps, the last of which is sqrt(squares), and each one is printed on the page with its numbers filled in. The formula is the one published by Wolfram MathWorld, not an approximation fitted to it.
Formula and sources checked · How we check
Leg a 3 ft, Leg b 4 ft
5.000 ft
Hypotenuse for the example below. Editing a field recomputes the calculator below; this figure holds the answer the page was loaded with.
It is written into the HTML rather than drawn by a script, so a search engine reading this page without running JavaScript still finds an answer.
- a² + b²
pow(a, 2) + pow(b, 2)25 sq ft- Hypotenuse
sqrt(squares)5 ft- Area
a * b / 26 sq ft- Perimeter
a + b + hypotenuse12 ft- Angle opposite leg a
atan(a / b) * 180 / pi36.87 °- Angle opposite leg b
90 - angle_a53.13 °
Worked example
Legs of 3 and 4 give a hypotenuse of exactly 5 — the smallest whole-number right triangle, and the reason a 3-4-5 measurement squares a corner on site without a square.
How to work it out yourself
- 1.Measure the two legs that meet at the right angle.
- 2.Square each and add them together.
- 3.Take the square root of that sum for the hypotenuse.
- 4.To check a corner is square instead, measure 3 along one wall and 4 along the other: the diagonal is 5 if the corner is true.
The formula
- a² + b²
pow(a, 2) + pow(b, 2) - Hypotenuse
sqrt(squares) - Area
a * b / 2 - Perimeter
a + b + hypotenuse - Angle opposite leg a
atan(a / b) * 180 / pi - Angle opposite leg b
90 - angle_a
Source: Wolfram MathWorld — right triangle, NIST Digital Library of Mathematical Functions
Questions people actually ask
- How do I square a corner without a square?
- Measure 3 ft along one edge and 4 ft along the other, then measure between those marks. It reads 5 ft when the corner is exactly 90°, and any multiple works — 6-8-10 is more accurate over a long wall.
- What if I know the hypotenuse and one leg?
- Subtract the square of the known leg from the square of the hypotenuse and take the root. The relationship runs in every direction.
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