Solve right triangles online
Right Triangle Calculator
Solve any side or angle of a right triangle instantly. Enter what you know and get the answer with full step-by-step working.
- No sign-up required
- Works offline
- 100% free
- Step-by-step solutions
Core calculator
Right Triangle Side Calculator
Result
Enter values to calculate the missing side or verify a triangle.
Show calculation steps
Recent calculations
Need the theory behind the arithmetic? Read the Pythagorean theorem before checking larger homework sets or classroom examples.
Full solver
Triangle Solver - All Cases
When you know two sides and an angle (SAS), two angles and a side (ASA/AAS), or all three sides (SSS), the solver finds every remaining measurement: sides, angles, area, and perimeter. It extends the main Pythagorean Theorem Calculator into a broader right-triangle workflow.
Triangle Solver
Supports SSS, SAS, ASA, AAS, and HL cases.
Formula reference
Right Triangle Formulas
The core equation of every right triangle calculator is a² + b² = c². Use these
cards to remember each rearrangement and copy the LaTeX form for class notes or documentation.
Step-by-step derivation
In any right triangle, the longest side is the hypotenuse. Square the two shorter sides, add them, and the sum equals the square of the hypotenuse. To find a missing leg, subtract the known leg square from the hypotenuse square and take the square root. That is why this Pythagorean theorem calculator can solve missing sides in either direction.
How it works
How to Use This Right Triangle Calculator
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Choose your known values
Select the tab that matches what you already know: two legs, one leg and the hypotenuse, or all three sides to verify.
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Enter the numbers
Type your values into the input fields. Choose a unit (meters, feet, inches, or centimeters) and set decimal precision if needed.
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Read the result
The missing side or angle appears instantly. The live diagram updates in real time so you can see the triangle take shape.
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Review the steps
Click "Show calculation steps" to expand the full working, with every formula substitution written out so you can copy it into your notes or homework.
Examples
Right Triangle Examples with Step-by-Step Solutions
Click any example to load it into the calculator above and see the full working automatically.
3-4-5 triangle
The classic starter example for a right triangle calculator.
Basic
5-12-13 triangle
A whole-number benchmark for checking calculator accuracy.
Basic
30-60-90 triangle
Recover the short leg from the hypotenuse in a classic special triangle.
Intermediate
Ladder against a wall
A practical word problem for finding a ladder length from wall height and floor distance.
Basic
FAQ
Frequently Asked Questions
A right triangle is a triangle that has exactly one 90-degree angle. The side opposite the right angle is called the hypotenuse and is always the longest side. The other two sides are called legs. Because one angle is fixed, right triangles follow predictable rules, including the Pythagorean theorem, that make them easy to solve with a calculator.
To fully solve a right triangle, you need at least two pieces of information, with at least
one being a side. If you need to find the hypotenuse,
use a² + b² = c². If you know one leg and the hypotenuse, rearrange
the formula to find the missing leg. If you know an angle and one side, use trigonometry.
This calculator handles all of those cases automatically.
Identify whether the missing side is a leg or the hypotenuse. If the hypotenuse is missing:
c = √(a² + b²). If a leg is missing:
a = √(c² - b²). Enter your known values in the calculator above and
it will apply the correct formula and show every step.
Yes. The Triangle Solver section on this page accepts side lengths and returns all three angles using inverse trigonometric functions. It also outputs area and perimeter. Select the SSS case and enter all three sides to get the full solution.
A right triangle has two legs, the sides that form the right angle, and one hypotenuse, the
side opposite the right angle. The hypotenuse is always longer than either leg. In the formula
a² + b² = c², a and b are the legs and
c is the hypotenuse.
Yes. Every calculation includes a step-by-step breakdown showing the formula, the substituted values, and the arithmetic. Click "Show calculation steps" below the result to expand the full working. This is useful for checking homework or understanding where the answer comes from.
The solver on this page supports five standard cases: SSS, SAS, ASA, AAS, and HL for right triangles. Select the case from the dropdown, enter the known values, and the solver returns all remaining sides, angles, area, and perimeter.
Yes, completely free. No account, no sign-up, and no paywall. All calculations run in your browser, and once the page has loaded you can keep using it offline.
Explore more
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30-60-90 Triangle Calculator
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45-45-90 Triangle Calculator
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Pythagorean Theorem
Learn the theorem, its proof, and real-world uses.