Calculator for Right-Angled Triangle

Formula

Pythagoras: hypotenuse c = √(a² + b²). Acute angles dey come from the sides: angle opposite leg a na arctan(a ÷ b), and angle opposite leg b na 90° minus that angle — the two acute angles always add to 90°. Area = ½ × a × b, and perimeter = a + b + c.

Example wey show the calculation

Legs 3 and 4: hypotenuse = √(3² + 4²) = √25 = 5. Angle opposite the side of 3 na arctan(3 ÷ 4) = 36.87°, so the other acute angle na 90 − 36.87 = 53.13°. Area = ½ × 3 × 4 = 6, and perimeter = 3 + 4 + 5 = 12. The 3–4–5 triangle na the smallest right triangle wey get whole-number sides. Na why you dey see am often for building sites and textbook questions.

Where e fit work and limits

This page dey take the two legs of right triangle. E no solve triangles if na hypotenuse and one leg you know, or angle and one side — for those ones, use Pythagoras or trigonometry directly with the same formulas above. E assume angle between the two sides wey you enter na exactly 90°; these formulas no apply to other triangles. We show angles in degrees to two decimal places.

Version of di formula: f0697a60d4c3 · Example don get check: 2026-10-31

Questions wey people dey ask often

Why a² + b² = c²?

Na Pythagoras' theorem: for right triangle, the square on the hypotenuse get the same area as the two squares on the legs together. E hold for every right triangle, no be only the ones with whole-number sides.

Wetin be 3–4–5 triangle?

Na the smallest right triangle with whole-number sides: 3² + 4² = 9 + 16 = 25 = 5². Builders don use ropes wey dem knot in 3–4–5 proportions for thousands of years to set exact right angles, because any multiple (6–8–10, 9–12–15) dey work the same way.

How we dey find the angles?

From the ratio of the legs: angle opposite leg a satisfy tan(angle) = a ÷ b, so angle = arctan(a ÷ b). The second acute angle na 90° minus the first, because triangle angles add to 180° and the right angle don take 90° already.

I fit enter hypotenuse instead of another side?

No be for this page — e expect two legs. If you know hypotenuse c and one leg a, the other leg na √(c² − a²). You fit calculate am, then enter am here.

The units matter?

Just make sure both legs use the same unit: hypotenuse and perimeter go come out for that unit, and area for its square. Mixing metres and centimetres dey give wrong answer, so convert first.

What about triangles wey no get right angle?

Pythagoras no apply. General triangles need law of cosines (c² = a² + b² − 2ab·cos C) or Heron's formula for the triangle area calculator, depending on wetin you know.

Other tools wey relate to dis

• Calculator for circle — area, circumference and diameter from radius
• Calculator for square area — area and perimeter of rectangle
• Tool to convert length units — metres, feet, inches and other length units