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Pythagorean Hypotenuse Calculator

Hypotenuse: -
Visual representation

Pythagorean Hypotenuse Calculator diagram

The diagram updates with your entries and is illustrative, not necessarily drawn to scale.

Calculation explained

How this result was calculated

The formula, your substituted values, and the evaluated result are shown below.

Visual analysis

How the result changes when the first input changes

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This calculator applies the pythagorean hypotenuse relationship. Enter values in the stated units and review the result. Check assumptions and use appropriate professional guidance for safety-critical decisions.
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About this calculator

Calculate pythagorean hypotenuse using clearly labelled inputs.

Calculator guide

How the Pythagorean hypotenuse calculator works

In a right-angled triangle, the square of the longest side (the hypotenuse) equals the sum of the squares of the other two sides. The calculator rearranges that:

Hypotenuse c = √(a² + b²)

Sides a and b must be in the same unit, and the answer comes out in that unit.

Worked examples

  1. The classic triangle: a = 3, b = 4, so c = √(9 + 16) = 5
  2. Diagonal of a 6 m × 8 m slab: √(36 + 64) = 10 m
  3. Ladder reach: a ladder whose foot is 1.2 m from the wall and reaches 4.8 m up has a length of √(1.44 + 23.04) = 4.95 m

Squaring up a corner with 3-4-5

Builders use Pythagoras every day to check that corners are square: 1. Measure 3 units along one side (e.g., 1.2 m) and mark it. 2. Measure 4 units along the other side (1.6 m) and mark it. 3. The diagonal between the marks should be exactly 5 units (2.0 m).

For bigger layouts, scale it up (6-8-10 or 9-12-15), or check that both diagonals of a rectangle are equal.

Finding a missing short side

If you know the hypotenuse and one side, then b = √(c² − a²). A 5 m ladder with its foot 1.25 m out reaches √(25 − 1.5625) = 4.84 m up the wall. Ladder safety guidance commonly suggests about a 4:1 ratio of height to base distance.

In 3D

The space diagonal of a box is √(length² + width² + height²). For a room 5 × 4 × 2.7 m, that's √(25 + 16 + 7.29) = 6.95 m, so a 7 m pipe won't fit through diagonally.

What is the Pythagorean theorem?

In a right-angled triangle, a² + b² = c², where c is the hypotenuse (the side opposite the right angle).

How do I check a corner is square?

Measure 3 m along one side and 4 m along the other. The diagonal between those points should be exactly 5 m.

Does Pythagoras work for all triangles?

Only right-angled triangles. For other triangles, use the cosine rule.

Written by Sam Alex, civil engineer. About the author