Right Triangle Calculator - Free Online Calculator
Solve a right triangle - one angle is exactly 90°. Find the hypotenuse, missing leg, area, perimeter and the two acute angles.
- Formula shown on the page
- Runs in your browser
- Your inputs stay private
Hypotenuse
5
Leg a
3
Leg b
4
Area
6
½ × a × b
Perimeter
12
Angle opp. a
36.8699°
Angle opp. b
53.1301°
Understanding the Right Triangle Calculator
Some math calculations come up often enough that reaching for a formula sheet or spinning up a spreadsheet feels like overkill. The Right Triangle Calculator handles this one end-to-end: enter your values, get the result, and see the formula beside it so you can verify the working or use it as a reference. The calculation runs in your browser with no sign-up and no internet dependency once the page has loaded.
The formula is shown above the result on purpose - it lets you trace the output back by hand if you ever want to. For the overwhelming majority of real-world inputs, the precision is more than sufficient. Edge cases worth knowing: domain restrictions (like logarithms of non-positive numbers, or division by zero) are flagged clearly, and the Right Triangle Calculator will tell you when an input doesn't make mathematical sense rather than returning a silent wrong answer.
Using the Right Triangle Calculator in 3 steps
Pick what you know: two legs, or hypotenuse and one leg.
Enter the values.
Read the missing side, area, perimeter and angles.
How the Right Triangle Calculator works
When two legs are given, the hypotenuse comes from the Pythagorean theorem: c = √(a² + b²). Angles come from atan(opposite/adjacent). Area = ½ × leg × leg.
c = √(a² + b²) Area = ½ × a × b Angle opposite a = arctan(a / b)
- a, bLegs (the two perpendicular sides)
- cHypotenuse (opposite the right angle)
How the Right Triangle Calculator gets its answer
The Right Triangle Calculator implements the textbook formula for right triangle calculator. Each step the calculator performs is mechanical and deterministic - you can trace the result through the formula by hand and arrive at the same number. For tools where multiple methods exist (e.g., different formulas for area or perimeter, different conventions for rounding), the Right Triangle Calculator either lets you pick the variant or defaults to the most widely-taught one.
Floating-point arithmetic has well-known quirks (e.g., 0.1 + 0.2 ≠ 0.3 exactly), but for typical problems the result is accurate to far more decimal places than you'll display. Where exactness is critical and inputs are integers or rationals, switch to the relevant exact-arithmetic tool on this site.
When to use the Right Triangle Calculator
- Students at school or college using the Right Triangle Calculator to check homework, prepare for exams, or build intuition through trial and error.
- Teachers and tutors using the Right Triangle Calculator as a live demonstration tool - open it on a projector, walk through the inputs, and the answer is visible to everyone.
- Engineers, analysts and developers using the Right Triangle Calculator for one-off calculations where pulling out a programming language or spreadsheet would be overkill.
- Curious users exploring how a number changes as one input varies - useful for understanding the underlying relationship at an intuitive level.
Common mistakes and gotchas
- Mixing units. Most math formulas are unit-agnostic; the calculator returns the numbers you give it, so consistency is your responsibility.
- Treating the result as exact when the inputs are approximate. Rounded inputs lead to rounded outputs.
- Misreading the formula. Spending 30 seconds reading the formula above the form removes most of the surprises later.
- Forgetting that some math formulas have domain restrictions - log of a non-positive number, square root of a negative, division by zero - the Right Triangle Calculator flags these but the underlying meaning is yours to interpret.
Get more out of this tool
- Try edge-case inputs (zero, very large, negative where applicable) to understand how the calculator behaves at the limits.
- Bookmark the page. The URL is stable and the tool works offline once loaded.
- Use the formula shown above the calculator to verify by hand at least once - it builds confidence in the tool and your understanding.
- Pair this calculator with related math tools on this site to chain calculations together for multi-step problems.
Questions about the Right Triangle Calculator
Which side is the hypotenuse?
Always the longest side - opposite the right angle. The other two are called legs (or cathetus).
What's a Pythagorean triple?
Three integers (a, b, c) satisfying a² + b² = c². Common examples: (3, 4, 5), (5, 12, 13), (8, 15, 17). Useful in carpentry to mark perfect right angles.
How do I find a leg given hypotenuse and other leg?
Rearrange Pythagoras: missing leg = √(c² − known²). The leg must be smaller than the hypotenuse.
Are the two acute angles complementary?
Yes - they sum to 90° because all three angles must sum to 180° and one is already 90°.
Where do right triangles appear in real life?
Construction (squaring corners), navigation (line-of-sight calculations), trigonometry foundations, screen/display dimensions (diagonal from width and height).
Difference from general triangle calculator?
Right triangles have one fixed angle (90°), so two pieces of info (two sides) determine the whole triangle. General triangles need three pieces.
Math in your browser
From simple percentages to scientific notation, statistics, geometry and big-number arithmetic - every common math problem you'd reach for a calculator for, runs in your browser with no installs. The fraction calculator preserves exact rationals, the big-number calculator uses BigInt for hundreds of digits without precision loss, and the scientific calculator's expression evaluator is a hand-written shunting-yard parser (no eval) that supports trig, log, factorial and parentheses.
If you're a student, double-check your work without paying for a graphing calculator. If you're a professional, use these tools as a sanity check on spreadsheet formulas. Every result is shown alongside its formula and inputs, so the math is always auditable.
The Right Triangle Calculator is part of the Math suite on Online Calculator Tools, alongside 6 related calculators. All tools share the same UI patterns, the same privacy-first rendering (nothing is sent to a server), and the same commitment to showing the formula and assumptions behind every result.