Skip to content
Math & Statisticsgeometry

Pythagorean Theorem Calculator

The missing side of a right triangle, whichever one it is, with the angles and area that follow. The 3-4-5 form is how a corner gets squared on site without a set square, and the page checks whether a measured corner is true.

Also called: hypotenuse calculator, right triangle calculator.

Missing side
5

The missing side is 5. The angles are 36.87 and 53.13 degrees, the area is 6 and the perimeter 12. Solved for the hypotenuse from the two legs. To square a corner, measure three units one way and four the other. A diagonal of five means the corner is true.

Angle opposite a
36.87
Angle opposite b
53.13
Area
6
Perimeter
12
Inscribed circle radius
1
Height to the hypotenuse
2.4
On Pythagorean triples
All three sides are whole numbers, which makes this a Pythagorean triple and useful for setting out on site.
Which side was found
Solved for the hypotenuse from the two legs.
On checking a square corner
To square a corner, measure three units one way and four the other. A diagonal of five means the corner is true.
How this is calculated
Method and background

How this is calculated

Give any two sides and the third follows. Leaving the hypotenuse blank solves for it; giving the hypotenuse and one leg solves for the other. Everything else comes free: the angles from the arctangent of the legs, the area as half their product, and the altitude to the hypotenuse as their product over it. The practical use is squaring a corner: measure three units along one wall and four along the other, and the diagonal is five if the corner is true.

rearranged for whichever side is missing, so the same relation solves all three cases
a, b, c
The two legs and the hypotenuse

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

a 3-4-5 triangle

Side a
3
Side b
4
Hypotenuse c, if that is what you know
0
Tolerance for a square corner check
0

Missing side5

the classic triple; the inradius of a right triangle is (a + b - c)/2

Open this example

solving for a leg instead

Side a
0
Side b
4
Hypotenuse c, if that is what you know
5
Tolerance for a square corner check
0

Missing side5

boundary: the hypotenuse was given, so the missing leg is 3

Open this example

Method and limits

What it assumes

  • A right angle between the two legs, which is what the theorem requires.

What it deliberately does not model

  • The relation holds only for right triangles; use the cosine rule otherwise.
  • On site, measurement error matters more than arithmetic, which is why the tolerance check exists.

Formula version 1.0.0 · definition 1.0.0 · India · Report a problem with this calculator

Frequently asked questions

Can I find a leg rather than the hypotenuse?
Yes. Give the hypotenuse and one leg and leave the other blank. The same relation rearranges, and the hypotenuse is always the longest side.
How do I square a corner without a set square?
Measure three units along one wall and four along the other. If the diagonal between those marks is exactly five, the corner is square. Any multiple works, and larger is more accurate.