Pick a calculator by what you already know. For any two sides of a right triangle, use the Pythagorean theorem calculator. When an angle is involved, use the right triangle solver; to test three lengths, use the checker; for points on a graph or the diagonal of a box, use the distance or 3D calculators. Every tool shows its working.
Which calculator do I need?
| Your question | Calculator | You enter |
|---|---|---|
| I know two sides of a right triangle. What is the third? | Pythagorean theorem calculator | Any two of a, b, c |
| I know both legs. How long is the hypotenuse? | Hypotenuse calculator | a and b, a leg and an angle, or the area and a leg |
| I know the hypotenuse and one leg. What is the other leg? | Missing side calculator | c and a or b |
| I know a side and an angle, or I need the angles too. | Right triangle solver | Any two of a, b, c, A, B |
| Do these three lengths make a right triangle? | Right triangle checker | Three sides |
| How far apart are two points? | Distance formula calculator | Two points in 2D or 3D |
| How long is the diagonal of a box or room? | 3D diagonal calculator | Length, width, height |
| What is the diagonal of a rectangle or square? | Rectangle diagonal calculator | Length and width |
| Which whole numbers fit a2 + b2 = c2? | Pythagorean triples generator | A limit, or a number to search for |
| How do I simplify a root like √72? | Simplify square roots | The number under the root |
| What are the sides of a 30-60-90 or 45-45-90 triangle? | Special right triangle calculator | One side |
| How wide and tall is a 65-inch TV? | Screen size calculator | Diagonal and aspect ratio |
| How long a ladder do I need? | Ladder calculator | Any two of ladder, height, base |
| How long are my roof rafters? | Rafter and roof pitch calculator | Run and pitch, or run and rise |
All calculators
- CalculatorsPythagorean Theorem CalculatorFree Pythagorean theorem calculator. Enter any two sides of a right triangle to find the third, with step-by-step working, exact radical answers and a drawing.
- CalculatorsHypotenuse CalculatorFree hypotenuse calculator: find the longest side of a right triangle from two legs, a leg and an angle, or the area and a leg, with steps and exact radicals.
- CalculatorsMissing Side Calculator (Find a Leg)Find the missing side of a right triangle from the hypotenuse and one leg. Enter b and c to get a, or a and c to get b, with steps, exact radicals and a check.
- CalculatorsRight Triangle Calculator and SolverRight triangle solver: enter any two values, such as two sides or a side and an angle, to get all three sides, both angles, area, perimeter, altitude and radii.
- CalculatorsIs It a Right Triangle? Checker and Triangle ClassifierIs it a right triangle? Enter three side lengths to check the triangle inequality, classify the triangle as right, acute or obtuse, and find all three angles.
- CalculatorsDistance Formula CalculatorFree distance formula calculator for 2D and 3D points. Get the distance with steps, the exact radical answer, the midpoint, the slope and a graph.
- Calculators3D Pythagorean Theorem CalculatorFind the space diagonal of a box from its length, width and height, or a missing side from the diagonal, with steps, exact answers and face diagonals.
- CalculatorsPythagorean Triples GeneratorGenerate every Pythagorean triple up to any hypotenuse, use Euclid's formula, check whether three numbers form a triple, or find all triples with a number.
- CalculatorsSimplify Square Root CalculatorSimplify any square root to simplest radical form, with the prime factorization, a factor tree and every step. Works for √n and k√n and gives the decimal.
- CalculatorsSpecial Right Triangle CalculatorSolve any 30-60-90 or 45-45-90 triangle from one side. Get the other sides in exact radical form and as decimals, plus area, perimeter and steps.
- CalculatorsRectangle Diagonal CalculatorFree rectangle diagonal calculator. Enter any two of length, width and diagonal to get the third, plus the diagonal angle, square mode and full working.
- CalculatorsScreen Size Calculator for TVs and MonitorsTV and monitor screen size calculator. Turn a diagonal and aspect ratio into width, height and area in inches and cm, get PPI, and compare two screens.
- CalculatorsLadder Calculator: Length, Height and AngleLadder calculator. Enter any two of ladder length, height on the wall and base distance to get the third and the angle, checked against the 4-to-1 safety rule.
- CalculatorsRafter Length and Roof Pitch CalculatorRafter length and roof pitch calculator. Enter the run and the pitch, rise or angle to get rafter length with overhang, roof angle, slope percent and slope factor.
Learning the method rather than checking an answer? Start with how to do the Pythagorean theorem, then use a calculator to check each step.
Exact answers or decimals?
When c2 is a perfect square, the answer is exact as it stands: legs 6 and 8 give 10. Most of the time it isn't. Legs of 5 and 5 give c = √50, which simplifies to 5√2. That radical is the exact answer; 7.07 is an approximation of it.
- In math class, give the exact value in simplest radical form unless told to round. See square roots and radicals for the method.
- In measuring jobs, round the decimal to a precision you can actually mark or cut.
- In multi-step problems, carry the exact value forward. Our right-triangle calculators accept inputs such as
5√2orsqrt(50)for this reason.
How to round
The nearest tenth is one decimal place, the nearest hundredth two, the nearest thousandth three. Here is √2 = 1.41421356… at each level:
| Rounded to | Value |
|---|---|
| the nearest whole number | 1 |
| the nearest tenth | 1.4 |
| the nearest hundredth | 1.41 |
| the nearest thousandth | 1.414 |
| four decimal places | 1.4142 |
Two rules prevent most rounding errors:
- Round once, at the end. Suppose a triangle with legs 1 and 1 has hypotenuse √2, and that hypotenuse becomes a leg of a second triangle whose other leg is 1. The exact answer is √2 + 1 = √3 ≈ 1.7321. Round √2 to 1.4 first and you get √1.96 + 1 = √2.96 ≈ 1.7205, off by more than a hundredth. (This chain of triangles starts the spiral of Theodorus.)
- Match the precision of the data. Lengths measured to the nearest tenth of a meter don't justify six decimal places. Round to the same precision and write ≈.
Units
The Pythagorean theorem needs every length in the same unit. Convert first, then calculate. For legs of 3 ft and 8 in, work in inches: 36 in and 8 in give c = √1,296 + 64 = √1,360 = 4√85 ≈ 36.88 in, a little over 3 ft. Areas come out in square units (in², ft², m²), and perimeters and diagonals in the original unit.
The exact conversions you need most are 1 ft = 12 in, 1 yd = 3 ft, 1 mi = 5,280 ft and 1 in = 2.54 cm. The units menu in our calculators only labels the answer; it never converts. Angles are always in degrees.
Frequently asked questions
Are these calculators free?
Yes, with no sign-up. They run entirely in your browser, so nothing you type is sent anywhere.
Should I give the exact answer or the decimal?
Follow the question: "simplest radical form" means 5√2, "to the nearest tenth" means 7.1. With no instruction, math teachers usually expect the exact form, and real-world problems a rounded decimal with units.
Can I share a calculation with someone?
On the Pythagorean theorem, hypotenuse, missing side, solver and checker pages, the page address updates as you type. Copy it, and the link opens with the same numbers filled in.
Do any of these work for triangles without a right angle?
The right triangle checker accepts any three sides and classifies the triangle as right, acute or obtuse, with all three angles. To find a missing side of a general triangle, use the law of cosines.
Keep exploring
- CalculatorsPythagorean Theorem CalculatorFree Pythagorean theorem calculator. Enter any two sides of a right triangle to find the third, with step-by-step working, exact radical answers and a drawing.
- CalculatorsRight Triangle Calculator and SolverRight triangle solver: enter any two values, such as two sides or a side and an angle, to get all three sides, both angles, area, perimeter, altitude and radii.
- LearnHow to Do the Pythagorean Theorem, Step by StepHow to do the Pythagorean theorem in 8 steps: label the sides, add or subtract the squares, take the square root and check. Flowchart and worked examples.
- CalculatorsSimplify Square Root CalculatorSimplify any square root to simplest radical form, with the prime factorization, a factor tree and every step. Works for √n and k√n and gives the decimal.
- PracticePythagorean Theorem ExamplesFifteen Pythagorean theorem examples solved step by step, from finding the hypotenuse to 3D diagonals, coordinates and algebra, each with a diagram and answer.
- PracticePythagorean Theorem Cheat SheetPrintable Pythagorean theorem cheat sheet: the formula and its rearrangements, the converse, special right triangles, triples, distance formulas and squares.