Right Triangle Calculator
Enter any two values of a right triangle and solve for all sides and angles instantly.
By Syed Mubashir Ali · Last updated
Worked example: what length ladder do you need?
Your gutters are 4 metres up and the ladder must stand 1.5 metres out from the wall for stability. That is a right triangle with legs 4 and 1.5. Enter both, solve, and the hypotenuse is √(16 + 2.25) = √18.25 ≈ 4.27 metres. Buy a 5-metre ladder. You want length to spare, and ladders are sold in round sizes anyway.
The angle at the ground is arctan(4/1.5) ≈ 69.4°. Ladder safety guidance says around 75°, so move the base slightly closer: 1.07 metres out gives exactly 75°. This is the kind of problem the solver exists for: two measurements you can take, one answer you actually need.
Two values are enough, but only the right two
Two sides, or one side and one acute angle: either pair determines the whole triangle. What does not work is two angles, because the right angle is already fixed and the two acute angles determine each other: knowing both tells you the shape but nothing about the size. A triangle with angles 36.87° and 53.13° could be 3-4-5 or 30-40-50.
One side alone is not enough either, for the same reason: infinite similar triangles share a single side length. The rule is simple: at least one of your two knowns must be a side, and then everything else follows from Pythagoras and the trigonometric ratios.
How to Use Right Triangle Solver
- 1Choose your unit: metres or feet and inches.
- 2Enter any two known values: two sides, or one side and one acute angle.
- 3Press Solve.
- 4Every remaining side and angle is calculated, along with the area.
- 5Use Reset to clear and start again. Angles A and B must each be between 0° and 90° and must sum to 90°.
- 6Sanity-check the result with Pythagoras: a² + b² should equal c². If it doesn't, one of your inputs was wrong.
Frequently Asked Questions
How many values do I need to give it?
Two, as long as at least one is a side. Two angles alone define the shape but not the size, so the triangle can't be solved from them: with a right angle already fixed, two acute angles just restate each other.
Why must angles A and B add to 90°?
Because the three angles of any triangle sum to 180° and one of them is already the right angle. The solver rejects a pair that does not sum to 90° because such a triangle cannot exist.
Which side is the hypotenuse?
Side c, opposite the right angle, and it is always the longest. If a calculation gives you a hypotenuse shorter than one of the other sides, one of your inputs is wrong.
Can I use it for non-right triangles?
No. It assumes a 90° angle. For other triangles you need the sine rule or the cosine rule, which need three values rather than two.
Does it handle feet and inches?
Yes. Choose the imperial unit and each side takes a feet value and an inches value separately, so you can enter measurements as they were taken rather than converting to decimal feet first.
Can you show a worked example?
Take the classic 3-4-5 triangle. Enter a = 3 and b = 4, press Solve, and you get c = 5, angle A ≈ 36.87°, angle B ≈ 53.13°, area = 6. Check: 3² + 4² = 9 + 16 = 25 = 5². The angles sum to 90° as they must. If your inputs produce something that fails the Pythagoras check, the inputs are wrong, not the solver.
What if I know the area and one side?
That is enough. Area = ½ × a × b, so the other leg is (2 × area) / known side. Enter both legs and solve as normal. For example, area 24 and side 6 gives the other leg as 48/6 = 8, and the hypotenuse follows: √(36 + 64) = 10. Another 6-8-10 triangle: scaled 3-4-5, which is no coincidence.
Why does it reject angles that do not sum to 90°?
Because no such triangle exists. The angles of any triangle sum to 180°, one is already 90°, so the other two must sum to 90°. There's no triangle with acute angles of 40° and 60° and a right angle. The solver refuses rather than giving you numbers for an impossible shape.
About Right Triangle Solver
The Right Triangle Solver finds every unknown side and angle from any two known values, and gives you the area as well. It runs entirely in your browser.
The rule to remember is that one of your two values must be a side. Two angles fix the shape of a triangle but not its size, and with the right angle already accounted for, the two acute angles simply determine each other, so there's nothing left to calculate.
It validates the inputs rather than producing a nonsense answer: each acute angle must fall between 0° and 90°, and the two must sum to 90°. A pair that does not describes a triangle that cannot exist, and the solver says so.
Feet-and-inches entry is handled as two separate fields per side, so site measurements go in as they were taken. Everything else follows from Pythagoras and the basic trigonometric ratios: the useful part is having all of it at once rather than working through each relation.
The 3-4-5 triangle is worth knowing by heart, because scaled versions of it appear constantly: 6-8-10, 9-12-15, 5-12-13 is a close cousin. When the solver returns clean integers, you are probably looking at one of these, and recognising it lets you skip the calculator next time. Carpenters use the 3-4-5 rule to check square corners: measure 3 feet along one edge, 4 along the other, and the diagonal must be 5 feet. Same triangle, no batteries required.