Pythagorean Theorem Tool

Calculate any missing side of a right triangle using two known sides. Explore a draggable triangle, view both acute angles, area, perimeter, squared lengths and step-by-step working, then export your results in several useful formats.

units
units
units
Calculated side
c = 5.000
c = √(a² + b²)
Interactive triangleDrag a vertex to explore dimensions
The draggable vertex adjusts both legs. Values update immediately; press Calculate to record the action.
Area6.000 units²
Perimeter12.000 units
Angle A36.870°
Angle B53.130°
Side lengths and squares
SideLengthSquare
Calculation steps

Table of Contents

  1. How Pythagorean Theorem Tool Works?
  2. Practical Use Cases
  3. Accuracy and Limitations
  4. Frequently Asked Questions (FAQs)
  5. Cite This tool

Highlights

  • Solve for either leg or the hypotenuse.
  • Explore a draggable, responsive right-triangle diagram.
  • See area, perimeter and both acute angles.
  • Review step-by-step solutions and side-length comparisons.
  • Export results as SVG, CSV, JSON or TXT.

How Pythagorean Theorem Tool Works?

For a right triangle, the squares of the two perpendicular legs, a and b, add up to the square of the hypotenuse c, which is opposite the 90° angle.

a2+b2=c2

Enter any two side lengths and select the missing side. The appropriate rearrangement determines the result:


Unknown sideFormula
Hypotenuse cc=a2+b2
Leg aa=c2−b2
Leg bb=c2−a2

With the default legs of 3 and 4, the hypotenuse is 5. The area is half the product of the legs, the perimeter is the sum of all three sides, and the acute angles come from inverse tangent.

Area=a×b2Perimeter=a+b+c
A=tan−1(ab)B=tan−1(ba)

Angles can be displayed in degrees or radians. The interactive diagram, squared-side table, comparison bars and calculation steps update to reflect the selected measurements and decimal precision.

Practical Use Cases

Carpenters and builders: Estimate the diagonal of a rectangular frame or confirm the required length of a diagonal brace from its perpendicular rise and run.

Surveyors and landscapers: Calculate a straight-line diagonal across a right-angled plot from two perpendicular distances.

Students and teachers: Practise finding an unknown leg or hypotenuse, then compare step-by-step calculations with the side-squared table and triangle diagram.

Designers and engineers: Check right-triangle dimensions, perimeter and area while examining how changing either leg affects both acute angles.

DIY and home renovators: Work out a ladder's sloping length from its vertical reach and horizontal offset, assuming those distances form a right angle.

Accuracy and Limitations

Results use JavaScript floating-point arithmetic and are displayed to the selected 0–10 decimal places, so rounded values may differ slightly from exact results. Both known sides must be finite, positive numbers; when finding a leg, the hypotenuse must exceed the known leg. The formulas apply only to right triangles, and extremely large inputs can exceed the numeric range. The diagram is a scaled visual aid rather than a precision drawing.

Frequently Asked Questions

In a right triangle, the squares of the two legs add up to the square of the hypotenuse: a² + b² = c².

Yes. Subtract the square of the known leg from the square of the hypotenuse, then take the square root.

The hypotenuse is opposite the 90° angle and is always the longest side of a right triangle.

No. It applies directly only to right triangles; other triangles require a more general relationship, such as the law of cosines.

They are three positive integers satisfying a² + b² = c², such as 3, 4 and 5.

Cite This tool