Right Triangle Calculator
Solve a right triangle from any two known values — two legs, a leg and the hypotenuse, or a side and an acute angle — for missing sides, angles, and trig ratios.
Calculator Inputs
Choose which two values of the right triangle you know.
Meaning depends on the mode above: leg a for "Two Legs", the hypotenuse (c) for "Leg + Hypotenuse" and "Hypotenuse + Angle", or leg a for "Leg + Angle".
Meaning depends on the mode above: leg b for "Two Legs", leg a for "Leg + Hypotenuse", or angle A in degrees (opposite leg a) for "Leg + Angle" and "Hypotenuse + Angle".
- Hypotenuse (c)
- 5.00
- Leg a
- 3.00
- Leg b
- 4.00
- Angle A (degrees)
- 36.87
- Angle B (degrees)
- 53.13
- sin(A)
- 0.60
- cos(A)
- 0.80
- tan(A)
- 0.75
- Formula Used
- c = √(a² + b²)
About these results
CalcSpectrum calculators produce automated estimates using established formulas and the specific values you enter. Because real-world outcomes depend on input accuracy, mathematical assumptions, and rounding conventions, please verify critical figures with an appropriately qualified financial, tax, medical, legal, or other professional, as relevant.
How It's Calculated
Formula
A right triangle has one 90-degree angle, so its two remaining angles (A and B) are always acute and always sum to exactly 90 degrees. Knowing any two values — two sides, or one side and one acute angle — is enough to solve for everything else: the Pythagorean theorem (a² + b² = c²) relates the three sides, and the basic trig ratios (sin A = a/c, cos A = b/c, tan A = a/b) relate a side pair to angle A. This calculator supports four known-value combinations: two legs, a leg plus the hypotenuse, a leg plus its opposite angle, or the hypotenuse plus angle A. Angle A is always the acute angle opposite side a (the leg referenced by whichever mode you choose); angle B is its complement.
Worked Examples
Two legs: a = 3, b = 4 (the classic 3-4-5 triangle)
- Hypotenuse: c = √(a² + b²) = √(9 + 16) = √25 = 5
- Angle A: tan⁻¹(a/b) = tan⁻¹(3/4) ≈ 36.87°
- Angle B: 90 − 36.87 ≈ 53.13°
- sin A = 3/5 = 0.6, cos A = 4/5 = 0.8, tan A = 3/4 = 0.75
Leg + angle: a = 3, angle A ≈ 36.87°
- Hypotenuse: c = a / sin(A) = 3 / sin(36.87°) ≈ 5
- Other leg: b = a / tan(A) = 3 / tan(36.87°) ≈ 4
- Angle B: 90 − 36.87 ≈ 53.13°
Frequently Asked Questions
How is this different from the Pythagorean Theorem Calculator?
The Pythagorean Theorem Calculator solves for exactly one missing side from two known sides — no angles involved. This Right Triangle Calculator additionally accepts a side plus an acute angle as your known values, and always reports both acute angles and the sin/cos/tan trig ratios alongside the missing sides.
How is this different from the Triangle Calculator?
The Triangle Calculator works with any three given side lengths for any triangle (not necessarily a right triangle), checking validity and computing area and side classification — it never solves for a missing value or an angle. This calculator always assumes a right angle and solves for whatever you didn't provide.
What does 'Angle A' mean in every mode?
Angle A is always the acute angle opposite the side labeled 'leg a' in whichever mode you selected — check each field's helper text for exactly which known value plays that role in the current mode. Angle B is simply 90° minus angle A.
Why does the calculator reject some leg + hypotenuse combinations?
The hypotenuse is always the longest side of a right triangle. If the hypotenuse value you enter isn't strictly greater than the known leg, those two numbers can't describe a real right triangle, so the calculator reports that clearly instead of taking the square root of a negative number.
Why must the angle be strictly between 0 and 90 degrees?
In any right triangle, the two non-right angles are always acute — each strictly between 0° and 90°. An angle of exactly 0° or 90° (or beyond) can't be one of those two angles, so it isn't a valid input for this calculator's angle-based modes.