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Triangle Calculator | Solve Sides, Angles, Area & Perimeter

Solve any triangle from three sides, two sides and an angle, or two angles and a side — the tool returns all missing sides, angles, area and perimeter. Right triangles use the Pythagorean theorem and oblique triangles use the sine and cosine laws, with full working shown.

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

Results

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

Quick reference

NeedFormula
Area from base/heightA = 1/2bh
Right triangle hypotenusec = √(a²+b²)
Perimetera+b+c
Angle sumA+B+C = 180°

functions Shows the working, not just the answer

For students and teachers, the final number is only half the value. Every math tool here exposes the formula it applied, the intermediate steps, and the rounding rule, so you can follow along, check your homework, or use the answer in a proof or report with confidence.

calculate Accurate to the spec

Calculations use 64-bit floating point with sensible rounding for the domain (currency to 2 decimals, percentages to 4 decimals, algebra to 6 significant figures). Where exact rational arithmetic matters — fractions, factorials, simplification — we use a dedicated BigNumber path so 1/3 + 1/6 returns ½, not 0.49999.

school Free for classroom use

Educators are welcome to link to any math calculator on CalcaTools from a class site, Google Classroom, or worksheet. The pages are mobile-friendly, free, ad-supported (so we can keep them free) and have no sign-up wall — students just click and use them in class or at home.

tips_and_updates Pair with the spoke articles

Below the calculator we link a small set of plain-English explainer pages — "What is a percentage?", "Why does PEMDAS matter?", and so on. They cover the underlying concept in 4–6 short paragraphs. Read those before the calculator if the topic is new, or after if you want the extra context.

Interpretation guide

Triangle typeClue
RightOne 90° angle
IsoscelesTwo equal sides
EquilateralThree equal sides and 60° angles

lightbulb Example — a right triangle with legs 3 and 4

By the Pythagorean theorem the hypotenuse is √(3² + 4²) = √25 = 5. The area is ½ × base × height = ½ × 3 × 4.

Result: Hypotenuse = 5, area = 6 square units.

What this means: This is the classic 3-4-5 right triangle — any triangle with sides in that ratio has a 90° angle.

Formula & methodology

Formula: Area = 1/2bh; a² + b² = c² for right triangles

The Triangle Calculator is built on a well-established calculation method. It uses the formula Area = 1/2bh; a² + b² = c² for right triangles to turn your inputs into a reliable result. Enter any combination of sides and angles — three sides, two sides and an included angle, or two angles and a side — and this triangle solver returns the remaining sides, all three angles, the area, and the perimeter. The steps are shown on the page so you can follow the reasoning from input to output.

Triangle solving depends on known inputs. Right triangles use Pythagorean relationships; general triangles may require law of sines or cosines.

How to use the Triangle Calculator

Enter any combination that defines the triangle — three sides, two sides and the included angle, or two angles and one side — and the tool solves for the rest. It applies the Pythagorean theorem a² + b² = c² for right triangles, the sine and cosine laws for oblique triangles, and the area formula ½ × base × height (or the sine-based area from two sides and the included angle). For a 3-4-5 right triangle, the hypotenuse is 5 and the area is 6 square units.

Interpreting your result

The solver returns all missing sides, all missing angles, the area, and the perimeter — the complete solution in one step. Triangles are the basic unit of measurement: land surveying splits plots into triangles, roof framing uses triangle geometry, and navigation and construction rely on the same angle-side relationships. The interior angles always sum to 180°, so the tool can often derive the third angle from two. The triangle inequality — any two sides must sum to more than the third — is enforced, and invalid input is flagged.

Common mistakes to avoid

The most common error is applying the Pythagorean theorem to a non-right triangle — it only works when one angle is exactly 90°. Second, entering sides and angles that cannot form a triangle, which the triangle inequality catches. Third, mixing units across sides — all sides must be in the same unit. Finally, misidentifying which angle is opposite which side: the sine law pairs each side with the angle opposite it, and switching them produces wrong answers.

Tips for best results

For right triangles, enter the two legs or a leg and the hypotenuse — the tool identifies the right angle automatically. When solving real measurements, sketch the triangle and label known values before entering them. Use the sine law when you know a side and its opposite angle; use the cosine law when you know two sides and the included angle. For construction layout, the 3-4-5 check confirms square corners. Double-check whether your input defines a unique triangle — three angles alone do not, since similar triangles share them.

Authoritative source: Wolfram MathWorld

Frequently asked questions

How do I use the triangle calculator?
Enter any combination that defines the triangle — three sides, two sides and the included angle, or two angles and one side — and the tool solves for the rest. It uses the Pythagorean theorem a² + b² = c² for right triangles and the standard area formula ½ × base × height. For a 3-4-5 right triangle the hypotenuse is √(9 + 16) = 5 and the area is 6.
What formula does the triangle calculator use?
The Triangle Calculator uses the standard Area = 1/2bh; a² + b² = c² for right triangles. You enter your values, and the calculator applies the formula step by step, showing the working so you can verify the math and understand how the result is derived rather than trusting a black box.
Is the triangle calculator accurate?
The Triangle Calculator applies the standard formula: Area = 1/2bh; a² + b² = c² for right triangles. 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.
Why do my results differ from another calculator?
The 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 combination of sides and angles — three sides, two sides and an included angle, or two angles and a side — and this triangle solver returns the remaining sides, all three angles, the area, and the perimeter. It applies the law of sines and law of There is no limit on usage, and it works on any device.
What does the Triangle Calculator do?
Enter any combination of sides and angles — three sides, two sides and an included angle, or two angles and a side — and this triangle solver returns the remaining sides, all three angles, the area, and the perimeter. It applies the law of sines and law of. 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.
Is the Triangle Calculator free and private?
Yes — the 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 Triangle Calculator?
The solver uses exact geometric relationships — the Pythagorean theorem, the sine and cosine laws, and the 180° angle sum — computed with full precision. Results are correct to the displayed precision for any valid triangle input. The accuracy in practice depends on how precisely you measured the sides and angles, since the laws propagate input errors into the outputs.

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