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Geometry Calculator with steps

Choose a shape, enter its measurements and get exact answers such as 9π or 6√6 alongside decimals, with the formula behind each one.

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Answer

Enter your numbers or pick an example — the answer and the steps appear here instantly.

Seven shapes, the formulas shown

  • Circle

    From the radius: area πr², circumference 2πr and diameter 2r, kept as multiples of π with decimals beside them.

  • Square

    Area s², perimeter 4s and diagonal s√2, all from a single side length.

  • Rectangle

    Area ab, perimeter 2(a + b) and diagonal √(a² + b²) in simplest radical form.

  • Triangle from three sides

    Area by Heron's formula, the perimeter and all three angles by the law of cosines. Sides that break the triangle inequality are rejected.

  • Right triangle from two legs

    Hypotenuse by the Pythagorean theorem in simplest radical form, plus the area ½ab and the perimeter.

  • Parallelogram and trapezoid

    A parallelogram gets area base × height and perimeter 2(a + b); a trapezoid gets its midsegment (a + b)/2 and area ½(a + b)h.

How to use the geometry calculator

  1. Select the shape

    The form then asks only for the measurements that shape needs.

  2. Enter the measurements

    Fractions like 5/2 and decimals like 2.5 both work. Use the same unit for every length.

  3. Calculate

    Each value appears with its formula. Exact forms come first, and rounded decimals carry ≈.

  4. Copy or explain

    Copy the answer, or send the problem to the AI Math Solver for a narrated solution you can question in AI Chat.

How Heron's formula works

Heron's formula gives a triangle's area from its three sides alone, with no height needed. First find the semi-perimeter s = (a + b + c)/2, then compute Area = √(s(s − a)(s − b)(s − c)).

Take sides 5, 6 and 7. The semi-perimeter is 9, so the area is √(9 × 4 × 3 × 2) = √216 = 6√6 ≈ 14.70. The largest angle of the same triangle sits opposite the longest side, and the law of cosines finds it: cos C = (a² + b² − c²)/(2ab) = (25 + 36 − 49)/60 = 0.2, so C ≈ 78.46°.

The formula only works for lengths that can actually close up into a triangle: each side must be shorter than the sum of the other two. With 2, 3 and 6, the semi-perimeter is 5.5 and s − c = −0.5, so the product under the root is negative and has no real square root. That is why the calculator rejects such inputs instead of returning an area.

Frequently asked questions

Exact answers keep π as a symbol so nothing is lost to rounding; a circle of radius 3 has area 9π. The decimal, about 28.27, is shown next to it and marked ≈.

Yes, when you give all three sides. The law of cosines turns the sides into angles in degrees, and you can confirm they sum to 180°.

It means the square root is written with no square factor left inside. √72 = √(36 × 2) = 6√2, so a right triangle with legs 6 and 6 has hypotenuse 6√2 ≈ 8.49.

Yes. Its area is base times perpendicular height, not the product of the two sides, so enter the height measured to side a. The slanted side b is used only for the perimeter.

No. Use one unit for every length; areas come out in that unit squared and perimeters in the unit itself.

The calculator is free, needs no account and computes in your browser. The AI explanation is optional: Pro plans include it* (*fair use: up to 300 runs a day across the writing, study and code tools), it costs 2 credits otherwise, and signed-out visitors can preview its opening. Like any AI writing it can contain errors, and it is meant for study, so check your course's rules before using it on graded work.

Other tools for geometry homework

Measure any flat shape

Pick a shape, enter the sides and get exact area, perimeter and more.

Calculate a shape
  • Exact π and radical forms
  • Triangle angles included
  • Fractions accepted