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Right Triangle Calculator | Solve sides, angles & area

Solve any right triangle from two sides or a side and an angle — the Pythagorean theorem finds the missing side, trigonometry the angles, and the area and perimeter follow. The complete solution with every step displayed.

Last updated: June 2026 · Free · No sign-up required

Results

Enter values above and click Calculate to see your result instantly.

Quick reference

KnownFind
Two legs a, bc = √(a² + b²)
Leg & hypotenuseother leg = √(c² − a²)
Side & angleUse sin, cos, tan
Area½ × a × b
AnglesA + B = 90°

info Right Triangle Calculator

Free math calculator — enter your numbers and get an instant, accurate result.

info Private by design

Everything runs locally in your browser. No uploads, no accounts, no tracking.

info Works everywhere

Fully responsive and mobile-friendly — calculate on any device, any time.

info Educational

Includes the formula and step-by-step explanation so you understand the math, not just the answer.

Interpretation guide

RelationshipTrig ratio
sin(A)opposite / hypotenuse
cos(A)adjacent / hypotenuse
tan(A)opposite / adjacent
Pythagorasa² + b² = c²
Acute anglesAlways sum to 90°

lightbulb Worked example

Let's say you are using the Right Triangle Calculator. Enter any two values of a right triangle — two sides, or a side and an angle — this calculator finds the remaining sides, both acute angles, the area, and the perimeter using the Pythagorean theorem Enter the values that match your situation into the input fields and press calculate — using realistic numbers makes the result directly useful for you.

Result: The calculator instantly applies the formula a² + b² = c² · tan(A) = opposite / adjacent and returns the result with appropriate precision.

What this means: Read the result in the context of what you are measuring. The step-by-step breakdown lets you confirm the math and understand which input most affects the outcome.

Formula & methodology

Formula: a² + b² = c² · tan(A) = opposite / adjacent

How the result is calculated

A right triangle has one 90° angle, so the Pythagorean theorem links the two legs and the hypotenuse, while the basic trig ratios connect the sides to the acute angles. Any two independent values fix the whole triangle.

  1. Identify which sides and angles you know (the right angle is always 90°).
  2. Use a² + b² = c² for a missing side, or sin/cos/tan for a missing angle.
  3. Find the remaining angle from A + B = 90° and the area as ½·a·b.

Example

Legs 3 and 4: hypotenuse c = √(9 + 16) = 5. Angle A = arctan(3/4) = 36.87°, B = 53.13°, area = ½ × 3 × 4 = 6.

What is the Right Triangle Calculator?

The Right Triangle Calculator is a free, browser-based math calculator tool that helps you Enter any two values of a right triangle — two sides, or a side and an angle — this calculator finds the remaining sides, both acute angles, the area, and the p. Instead of working through the math by hand or in a spreadsheet, you enter your values and the calculator returns an accurate result instantly — while still showing the formula and the steps so you can verify the reasoning. It is designed for quick everyday use: no sign-up, no installation, and everything runs locally in your browser for complete privacy.

How to use the Right Triangle Calculator

  1. Enter the required values into the input fields.
  2. Press the calculate button — the result appears immediately, updated live as you change any value.
  3. Read the step-by-step breakdown below the result to see exactly how the calculation was performed.
  4. Use the interpretation guide to understand what the result means for your situation, and try different inputs to see how they change the outcome.

How to use the Right Triangle Calculator

Enter any two values of a right triangle — two sides, or one side and one acute angle — and the tool finds everything else: the remaining sides via a² + b² = c², the angles via tan(A) = opposite ÷ adjacent, the area, and the perimeter. For example, a right triangle with legs 6 and 8 has a hypotenuse of 10, an area of 24, and acute angles of about 36.9° and 53.1°. The two acute angles always sum to 90°, so finding one gives the other free.

Interpreting your result

Right triangles are the most-used shape in practical math: roof pitches, ladder angles, ramp slopes, sight lines, and structural loads all reduce to right-triangle problems. The Pythagorean theorem relates the sides, and the trigonometric ratios (sine, cosine, tangent) connect sides to angles. The area formula ½ × base × height works with either leg as the base. Whether you are checking a wheelchair ramp's slope, a TV's diagonal, or a rafter's length, the calculator turns the known measurements into the missing ones in one step.

Common mistakes to avoid

The most common error is applying the Pythagorean theorem to a triangle that is not right-angled — it only holds when one angle is exactly 90°. Second, mislabeling the hypotenuse: c is always the side opposite the right angle, the longest side. Third, mixing units across the sides. Finally, entering two angles and a side in a way that confuses which side is opposite which angle — label the sketch before entering values.

Tips for best results

Sketch the triangle and label the known sides and angles before entering them. When you know one leg and the hypotenuse, the calculator finds the other leg — common for ladder problems. For ramps and roofs, convert the slope or pitch to an angle first, or use the side-based mode. Verify with a quick 3-4-5 check on any layout job: measure 3 and 4 along the two edges; if the diagonal is 5, the corner is square. Use the area output for tiling and material estimates.

Authoritative source: Wolfram MathWorld

Frequently asked questions

How do you solve a right triangle?
Enter any two values — two sides, or one side and one acute angle — and the tool finds the rest. The Pythagorean theorem a² + b² = c² handles the sides, while the angles come from tan(A) = opposite ÷ adjacent and the fact that the acute angles sum to 90°. Area and perimeter are also returned, so you get the complete solution in one step.
What is the Pythagorean theorem?
In a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs: a² + b² = c². It lets you find any side when the other two are known.
How do I find an angle in a right triangle?
Enter the required values into the input fields and press the calculate button. The tool applies the formula a² + b² = c² · tan(A) = opposite / adjacent and returns the result with a short explanation of each step, so you can check the working yourself.
What is a 3-4-5 triangle?
The Right Triangle Calculator is free, private, and accurate: it runs entirely in your browser (no uploads, no accounts), applies the standard calculation, and explains each step so you can verify the result. Enter any two values of a right triangle — two sides, or a side and an angle — this calculator finds the remaining sides, both acute angles, the area, and the perimeter using the Pythagorean theorem and SOH-CAH-TOA. It shows which trigonometric function was There is no limit on usage, and it works on any device.
How do I find the area of a right triangle?
Use the two legs as base and height: Area = ½ × leg₁ × leg₂, because in a right triangle the legs are perpendicular. For a 6-8-10 right triangle, the area is ½ × 6 × 8 = 24 square units. The hypotenuse is never used in this formula. The calculator returns the area alongside the sides and angles.
What does the Right Triangle Calculator do?
Enter any two values of a right triangle — two sides, or a side and an angle — this calculator finds the remaining sides, both acute angles, the area, and the perimeter using the Pythagorean theorem and SOH-CAH-TOA. It shows which trigonometric function was. The calculator takes your inputs, applies the standard calculation, and returns a clear result so you can make an informed decision without doing the math by hand.
What formula does the Right Triangle Calculator use?
It combines a² + b² = c² for the sides with tan(A) = opposite ÷ adjacent for the angles. Enter any two known values and the tool derives the remaining sides, both acute angles, the area, and the perimeter. For example, a right triangle with legs 6 and 8 has a hypotenuse of 10, an area of 24, and angles of about 36.9° and 53.1°.
Is the Right Triangle Calculator free and private?
Yes — the Right Triangle Calculator. There is no sign-up, no paywall, no trial, and no limit on how many calculations you can run. CalcaTools covers its costs with non-intrusive display advertising, so the calculator itself never asks for payment or restricts any feature.
How accurate is the Right Triangle Calculator?
The Right Triangle Calculator applies the standard formula: a² + b² = c² · tan(A) = opposite / adjacent. It is tested against published worked examples before launch and uses native double-precision arithmetic, so results are accurate to typical precision for the values you enter — with no intermediate rounding that could distort the answer.

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