Find the hypotenuse or a missing leg, plus area, perimeter, and both acute angles of a right triangle.
Enter your two known values and click Calculate to see the result.
This free right angle triangle calculator solves a right triangle completely from just two known measurements — either its two legs, or one leg plus the hypotenuse — instantly giving you the missing side, the area, the perimeter, and both acute angles. A right triangle is defined by having one angle fixed at exactly 90°, which is what makes the Pythagorean theorem (a²+b²=c²) apply, and why knowing any two of its three sides is always enough to find everything else. Whether you're checking a homework problem, squaring a construction corner, or solving a real-world right-triangle problem, this right angle triangle calculator shows the full working behind every result.
Every right triangle is fully determined by its two legs (the sides forming the right angle) — from them, the hypotenuse follows via the Pythagorean theorem, and so does the area, perimeter, and both acute angles. This calculator also accepts one leg plus the hypotenuse as an alternative starting point, working backward to find the missing leg first.
Students and teachers checking Pythagorean theorem and right-triangle homework, carpenters and builders squaring corners using the 3-4-5 method, DIYers calculating rafter or ramp lengths, and anyone who has two right-triangle measurements and needs the rest can use this tool.
The right triangle is the single most useful triangle type in applied mathematics, because any two-dimensional distance problem can be broken into perpendicular horizontal and vertical components, forming a right triangle. This is why the Pythagorean theorem — and by extension, this calculator — underlies distance formulas, navigation, physics, and structural engineering.
Carpenters and builders use the 3-4-5 rule (a right triangle with legs 3 and 4 and hypotenuse 5) to verify a corner is truly square. Roofers compute rafter length from the rise and run of a roof. Navigators and surveyors use right-triangle relationships to compute distances and bearings. Physics students resolve motion or force vectors into perpendicular components using the same math.
How the Pythagorean theorem unlocks every other measurement
A right triangle has exactly one 90° angle, leaving the other two acute angles to share the remaining 90° between them.
The hypotenuse sits opposite the largest (90°) angle, so it's always longer than either leg individually.
Since the two legs are already perpendicular, they can be used directly in the ½×base×height area formula with no extra height calculation needed.
From choosing a mode to verifying the result
Pick "Two Legs" if you know both legs, or "Leg & Hypotenuse" if you know one leg and the hypotenuse.
Type in the two known measurements for your chosen mode.
The calculator applies the Pythagorean theorem to find the missing side, then derives area, perimeter, and angles.
Review both legs, the hypotenuse, the area, the perimeter, and both acute angles.
Confirm the two acute angles sum to 90°, and that a²+b²=c² holds for your three sides.
The classic 3-4-5 right triangle
A builder wants to confirm a corner is square using legs of 3 meters and 4 meters. What should the diagonal (hypotenuse) measure, and what are the area, perimeter, and angles?
Explanation: If the measured diagonal is exactly 5 meters, the corner is confirmed square — this is exactly the "3-4-5 rule" builders have used for centuries to verify a right angle without any angle-measuring tools at all, just a tape measure.
What each output field represents
| Field | What It Means |
|---|---|
| Leg a, Leg b | The two sides that meet at the right angle |
| Hypotenuse | The longest side, opposite the right angle |
| Area | ½ × leg a × leg b, in squared units |
| Perimeter | The sum of all three sides |
| Angles | The two acute angles, always summing to exactly 90° |
Manual verification: square each leg, add them, and confirm the result equals the hypotenuse squared (a²+b²=c²) — the direct Pythagorean check. Also confirm the two displayed angles sum to 90°.
The hypotenuse is the side that sits opposite the 90° corner, and it is always the longest of the three sides. The legs are the two sides that actually meet to form the right angle — once you can spot those, the hypotenuse is the remaining side that connects their free ends.
Not for the hypotenuse, area, or perimeter — the Pythagorean theorem and the ½ × a × b area formula treat the two legs symmetrically, so swapping them changes nothing. It only affects the angle labels, because each acute angle is measured opposite its own leg.
A 30-60-90 right triangle always has its sides in the ratio 1 : √3 : 2 — the shortest leg (opposite the 30° angle), the longer leg (opposite the 60° angle), and the hypotenuse. Given any one side, you can scale that ratio to recover the other two in seconds.
Angle A is the acute angle opposite leg a — the corner that leg a does not touch — and Angle B is the acute angle opposite leg b. The two always sum to exactly 90°, which is a handy way to confirm you matched the labels correctly.
No — the calculator assumes both inputs share the same unit. Convert everything to a single unit first (for example, 50 cm to 0.5 m), and the results will come back in that unit for the sides and that unit squared for the area.
Because the legs meet at a right angle, one leg can serve as the base and the other as the height of the triangle directly — no separate height measurement is needed. That is why Area = ½ × a × b works for every right triangle.
Where right-triangle math shows up constantly
Check Pythagorean theorem and right-triangle problems step by step.
Verify a corner is square using the 3-4-5 method.
Calculate a safe ladder angle from its height and base distance.
Find rafter length from a roof's rise and run.
Compute straight-line distance from perpendicular displacement components.
Relate diagonal screen size to width and height.
Calculate ramp length from height and horizontal run.
Compute distances using perpendicular offset measurements.
Resolve motion or force vectors into perpendicular components.
Verify right-triangle component dimensions match design specs.
Lay out right-angle corners for courts and fields accurately.
Practice right-triangle problems common in SAT/ACT/GRE quantitative sections.
What this right angle triangle calculator does well, and where it doesn't apply
Whole-number right triangles worth memorizing
| Leg a | Leg b | Hypotenuse c |
|---|---|---|
| 3 | 4 | 5 |
| 5 | 12 | 13 |
| 8 | 15 | 17 |
| 7 | 24 | 25 |
Summary: This right angle triangle calculator gives you an instant, free way to find a right triangle's hypotenuse or missing leg, area, perimeter, and both acute angles — using the Pythagorean theorem, with the working shown. Pair it with the Pythagorean Theorem Calculator and Triangle Solver for related needs.
Common questions about right triangles
Trusted educational references to go deeper on the Pythagorean theorem
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