Two legs
a=9, b=12c = 15, area = 54, perimeter = 36
Right Triangle Calculator
Use this free right triangle calculator to enter two known sides and find the missing side, hypotenuse, area, perimeter, acute angles, formula steps, and private recent answers.
Unit-aware inputsFormula noteExample numbersTab-only history
Hypotenuse15 cm
- Area
- 54 cm^2
- Perimeter
- 36 cm
- Acute angles
- 36.8698976458 degrees, 53.1301023542 degrees
Steps
- Use the Pythagorean theorem to complete the side lengths.
- Use area = leg a x leg b / 2.
- Use sine ratios to find the two acute angles.
- The main result is 15 cm.
Recent answers
Recent right triangle answers will appear here.
Privacy note
Geometry answers and history stay in this browser tab while you work.
Copy answer only writes the current result to your clipboard when you press it.
How to use the Right Triangle Calculator
- Choose two legs or leg and hypotenuse mode.
- Enter the known side lengths and optional unit label.
- Press Calculate right triangle to find sides, area, perimeter, and acute angles.
- Use examples, recent answers, or copy the result while solving right triangles.
What people use it for
Complete a right triangle from two known side lengths.
Find hypotenuse, missing leg, area, perimeter, and angles together.
Check 3-4-5, 5-12-13, and other right-triangle examples.
Compare side, area, perimeter, and angle results before copying homework notes.
Catch impossible leg-and-hypotenuse inputs before trusting a result.
Copy right-triangle formula steps into notes or homework.
Quick examples
Leg and hypotenuse
leg=5, c=13missing leg = 12, area = 30
Classic 3-4-5
a=3, b=4angles are about 36.87 and 53.13 degrees
Construction diagonal
a=6 ft, b=8 ftdiagonal c = 10 ft
Decimal sides
a=7.5, b=10c = 12.5, area = 37.5
Invalid hypotenuse
leg=9, c=7invalid because c must be longest
Need the guide or a nearby tool?
Need a slower walkthrough, a related calculator, or the full library? These links keep you close to the task you started.
- How to use the Right Triangle CalculatorSee slower examples, input meanings, formula notes, result limits, and mistakes to avoid.
- CalculatorsBrowse related calculators and utilities in the same category.
- Calculator and utility guidesFind more guides that use real tool inputs and example numbers.
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Frequently asked questions
Quick answers about formulas, units, valid measurements, examples, copying, and private in-browser history.
What does the Right Triangle Calculator find?
It finds the missing side, hypotenuse, area, perimeter, and the two acute angles for a right triangle. The third angle is the fixed 90-degree angle.
What inputs can I use?
Use two legs mode when both legs are known. Use leg and hypotenuse mode when you know one leg and the hypotenuse. Keep every length in the same unit.
What do the main Right Triangle Calculator inputs mean?
The main inputs are the numbers, operation, mode, or known values the calculator needs. Keep units consistent, enter percentages the way the page label shows, and use the examples as a quick check before trusting the answer.
How should I read the Right Triangle Calculator answer?
Read the headline answer, then check the supporting lines and examples to understand how the calculator got there. If one input changes, rerun the tool and compare the new answer instead of guessing.
What should I double-check before trusting the Right Triangle Calculator?
Check units, signs, rounding, and the selected mode before copying the answer. If the number feels weird, rerun one of the examples first, then put your own values back in slowly.
What formulas does the calculator use?
For two legs, it uses a^2 + b^2 = c^2 to find the hypotenuse. For a missing leg, it subtracts the known leg squared from c^2, then takes the square root.
How are the angles calculated?
After the sides are known, the calculator uses trigonometry ratios to estimate the two acute angles. The two acute angles always add up to 90 degrees.
What formula is used for area?
Right triangle area uses A = leg a x leg b / 2 because the two legs are perpendicular base and height.
How is perimeter calculated?
Perimeter is the sum of all three side lengths: leg a + leg b + hypotenuse c. For a 9-12-15 triangle, the perimeter is 36.
What if my hypotenuse is shorter than the leg?
That cannot make a right triangle. The hypotenuse must be the longest side because it is opposite the 90-degree angle.
Can I enter decimals or units?
Yes. Decimal side lengths work, and the optional unit label is carried into the length, area, and perimeter results. Use one unit system at a time.
Why are some answers rounded?
Many right-triangle side lengths and angles do not end neatly. The calculator rounds long decimals but keeps the formula steps visible so you can check the math.
Which side is the hypotenuse?
The hypotenuse is the side opposite the 90-degree angle. It is always the longest side of a valid right triangle.
How is this different from the Pythagorean Theorem Calculator?
The Pythagorean Theorem Calculator focuses on one missing side. This calculator also shows area, perimeter, acute angles, and a fuller right-triangle summary.
Should I use the general Triangle Calculator instead?
Use the Triangle Calculator when the triangle is not guaranteed to have a 90-degree angle or when you have three side lengths and need a general triangle check.
Can this prove a real corner is square?
No. It only solves the measurements you enter. For real layout, measure carefully, keep units consistent, and confirm the corner is meant to be 90 degrees.
Is my right triangle history private?
Yes. Recent right triangle answers stay only in the current browser tab while you use the page. They are not sent to a server.