Right Triangle Calculator
Solve any right triangle from two known sides using the Pythagorean theorem. Get the missing side, area, perimeter and angles.
Hypotenuse c
5
Area
6
Perimeter
12
Angle A
36.87°
Angle B
53.13°
Missing side
—
Angles are in degrees; the two acute angles always sum to 90\u00B0. Uses the Pythagorean theorem a\u00B2 + b\u00B2 = c\u00B2.
Last updated: February 2026
How this calculator is verified
Checked by True Calculator automated test suite on
- Formula verified against a published worked example in the automated test suite
- Edge cases (zero, negative, boundary and unit-mismatch inputs) covered by unit tests
The full verification method is on our how we verify page. Found an error? Tell us and we will re-check it.
When to Use This Calculator
A right triangle calculator is valuable for students, builders, and anyone working with right angles. In Indian classrooms it supports geometry and trigonometry homework. Carpenters and masons use the 3-4-5 principle to check that walls, frames and tiles meet at perfect right angles. Electricians and plumbers estimate how much wire or pipe is needed diagonally across a room. Ladder users can find how high a ladder reaches against a wall when the base distance is known, which is also a safety check. Architects and interior designers calculate ramp slopes and staircase dimensions with it, and farmers and land surveyors compute triangular plot areas quickly. The calculator solves instantly with the Pythagorean theorem, so no trigonometric tables or manual square roots are needed, making it a dependable companion for exam practice and real construction work.
How to Use This Calculator
- Step 1: Choose what you know from the options: two legs, a leg and the hypotenuse, or the other leg and the hypotenuse.
- Step 2: Enter the two known side values; leave the unknown side empty.
- Step 3: Read the missing side, area, perimeter and both angles in the results panel.
- Step 4: Check that the hypotenuse shown is the longest side, which confirms a valid right triangle.
Worked Example
A carpenter in Bengaluru is building a wall shelf and needs a diagonal brace. The two legs of the right triangle are 3 m and 4 m, so he enters both with the two-leg mode selected. The calculator finds the hypotenuse as 5 m using the Pythagorean theorem, the area as 6 square metres and the perimeter as 12 m. The two angles come out as 36.87° and 53.13°, which sum to 90°. He cuts the brace at 5 m and checks the corner with the 3-4-5 rule, a classic trick builders use because 3² + 4² = 5² exactly.
Tips and Common Mistakes
- •Tip 1: The hypotenuse is always opposite the right angle and is the longest side, so its value must exceed both legs.
- •Tip 2: Use the two-leg mode when checking whether a corner is square with a 3-4-5 measurement.
- •Tip 3: For roof pitch or ramp work, the angles tell you the incline in degrees, which contractors can directly use.
- ✗Mistake 1: Entering a hypotenuse that is shorter than a leg, which makes the triangle impossible. The calculator shows a hint instead.
- ✗Mistake 2: Confusing the two legs when only one leg and the hypotenuse are known, since the order decides which angle belongs to which side.
Frequently Asked Questions
How does the right triangle calculator work?
It uses the Pythagorean theorem, a² + b² = c². Give any two sides and the third is computed, along with the area, perimeter and both acute angles.
Which side is the hypotenuse?
Side c is always the hypotenuse, the longest side opposite the right angle. In the "two legs" mode you enter sides a and b and the calculator finds c.
Can I find a leg when I know the hypotenuse?
Yes. Choose the mode with a leg and the hypotenuse, such as "leg + hypotenuse (a, c)". The other leg is found as the square root of c² − a².
Why do the two angles always add up to 90 degrees?
A right triangle has one 90-degree angle, and the three angles of any triangle total 180 degrees, so the other two must sum to exactly 90 degrees.
Where is a right triangle calculator useful?
Students use it for trigonometry homework, while builders and carpenters use it to check square corners, ramps and roof pitches. It also helps for ladder placement and diagonal measurements.
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