Right Triangle Calculator
Calculate the base, height, hypotenuse, acute angles, area, perimeter, and trig ratios of a right triangle from three common input setups.
Right Triangle Calculator
Use two legs, one leg plus the hypotenuse, or angle A plus one side to calculate base a, height b, hypotenuse c, both acute angles, area, and perimeter in one place. If you keep the same length unit for every input, the result stays in that same unit.
If you already know base a and height b, the calculator uses the Pythagorean theorem to find the hypotenuse and both angles right away.
The horizontal leg along the bottom of the triangle.
The vertical leg that meets the base at the right angle.
Choose which leg you already know so the other leg can be solved by subtraction under the square root.
Enter the actual length of the leg selected above.
The hypotenuse must be longer than either leg.
Angle A is the acute angle between base a and hypotenuse c.
Enter an acute angle greater than 0° and smaller than 90°.
The calculator uses trig ratios to recover the other two sides.
These presets help you inspect the layout and the formulas before entering your own values.
- In the leg + hypotenuse mode, the hypotenuse must stay longer than the known leg.
- Angle A is always interpreted as the angle between base a and hypotenuse c.
- You can use any length unit, but all inputs should stay in the same unit.
- The copy button is most useful after you run a real calculation instead of relying on the example state.
Check the inputs and press Calculate to update the triangle result.
A right triangle with base 3 and height 4 is the classic 3-4-5 case, so the area is 6 and the perimeter is 12.
This is a scaled preview of the triangle. Angle A is the acute angle between base a and hypotenuse c.
| Input setup | Two legs |
|---|---|
| Base a | 3 |
| Height b | 4 |
| Hypotenuse c | 5 |
| Altitude to c | 2.4 |
| Inradius | 1 |
- c = √(a² + b²) = √(3² + 4²) = 5
- Area = a × b ÷ 2 = 3 × 4 ÷ 2 = 6
- Angle A = arctan(b ÷ a) = arctan(4 ÷ 3) ≈ 53.13°
What is a right triangle calculator?
A right triangle calculator helps you solve the remaining side lengths and acute angles when one angle is fixed at 90°. If you already know part of the triangle, you can use the Pythagorean theorem and trigonometric ratios to recover the rest without setting up every formula by hand.
This version focuses on three practical setups: two legs, one leg plus the hypotenuse, and angle A plus one side. It also keeps the follow-up interpretation on the same screen by showing area, perimeter, altitude to the hypotenuse, inradius, and a scaled visual preview together with the raw side values.
Useful situations
Right triangles appear in school math, construction sketches, roof or ramp slope estimates, and quick distance checks. Switching the input setup to match the values you already know saves time and makes manual verification much easier. If you first need to organize similar triangles or side ratios before solving the right triangle itself, the Proportion Calculator is a natural first step.
- Homework and study – Check side lengths and angle results while reviewing trig and the Pythagorean theorem
- Slope planning – Estimate the side length of a ladder, ramp, or roof triangle from an angle and one known side
- Drawing and layout work – Fill in a missing side on a sketch when only two measurements are available
- Area checks – Use the base and height to estimate the half-rectangle area quickly
- Result review – Compare the visual preview, trig ratios, and formula steps in one place
Key features
The tool is designed to stay compact while still explaining the meaning of the result. The top result card highlights the hypotenuse and the most important interpretation first, then the lower sections keep the formulas, ratios, and support values easy to scan.
- Three input setups – Solve from two legs, one leg plus hypotenuse, or angle A plus one side
- Main geometry values – Base a, height b, hypotenuse c, both acute angles, area, and perimeter
- Support values – Altitude to the hypotenuse and inradius on the same screen
- Trig ratio panel – Shows sin A, cos A, tan A, and a Pythagorean check
- Scaled triangle preview – Helps you see the shape you just calculated
- Copy-ready result – Makes it easier to move the calculation into notes or messages
How to use it
Choose the setup that matches the information you already have, enter the known values, and run the calculation. The result updates the top summary, the preview, the table, and the step-by-step formulas together so you can review everything in one pass.
- Pick an input setup – Two legs, leg + hypotenuse, or angle A + one side
- Enter the known values – Keep every length in the same unit
- Set the decimal precision – Pick how much rounding you want to see
- Run the calculation – The triangle values, angles, and support metrics update together
- Review the formulas – Use the summary list to confirm how the result was derived
- Copy if needed – Send the result into notes, reports, or chat
Right triangle formulas in plain language
The core relationship is the Pythagorean theorem: a² + b² = c². If you know both legs, you can calculate the hypotenuse with c = √(a² + b²). If you know one leg and the hypotenuse, you can recover the missing leg with √(c² - known leg²).
When angle A is the acute angle between base a and hypotenuse c, the main trig ratios are sin A = b / c, cos A = a / c, and tan A = b / a. That means one acute angle plus one side is enough to rebuild the full triangle. If you want to compare the measured value of a side with the value you calculated here, the Percent Error Calculator is a good follow-up tool for the verification step.
The area is a × b ÷ 2, the perimeter is a + b + c, the altitude to the hypotenuse is (a × b) ÷ c, and the inradius is (a + b - c) ÷ 2. Keeping these support values on the same page makes the calculator useful not only for study but also for quick planning and layout work.
- Pythagorean theorem – a² + b² = c²
- Area – a × b ÷ 2
- Perimeter – a + b + c
- Altitude to c – (a × b) ÷ c
- Inradius – (a + b – c) ÷ 2
- Angle B – 90° – angle A
FAQ
Where is angle A in this calculator?
Angle A is the acute angle between base a and hypotenuse c. The other acute angle is shown as angle B and is always 90° minus angle A.
Why must the hypotenuse be longer than the known leg?
In every right triangle, the hypotenuse is the longest side. If the hypotenuse is not longer than the leg, the triangle cannot exist and the square-root subtraction would break.
Can I use any unit?
Yes. You can use centimeters, meters, feet, or any other length unit, as long as you keep the same unit for every side you enter.
Is angle A plus one side really enough?
Yes. In a right triangle, one acute angle and one side determine the rest of the shape because the trig ratios lock the remaining side relationships.
Can I check classic 3-4-5 or 5-12-13 triangles here?
Yes. The presets include a 3-4-5 case, and the leg + hypotenuse setup also makes it easy to confirm 5-12-13 style combinations.
Does changing the decimal places affect the actual calculation?
No. The calculator still uses the full numeric result internally and only rounds the values shown on screen to the precision you selected.
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