Geometry Shape Calculator

Choose any of 21 flat shapes and solids, type the measurements and instantly get area, perimeter, volume and surface area — with a labelled diagram drawn from your numbers and every substitution shown.

Class 5–10 13 plane + 8 solid shapes Live diagram Step-by-step

Area is the surface a shape covers and perimeter is the length of its boundary. A rectangle 8 cm by 5 cm has area 8 × 5 = 40 cm² and perimeter 2(8 + 5) = 26 cm. For solids, a cylinder of radius 7 cm and height 10 cm has volume πr²h = 1540 cm³.

Try an example:

Circle

Enter the measurements below.

Value of π
NCERT usually uses π = 22/7 when the radius is a multiple of 7.

Live diagram

Redrawn from your numbers as you type.

Drawn to scale
Area
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Formulas used

Step-by-step working

    All formulas at a glance
    ShapeFormulas
    How it works

    Mensuration made visual

    Every answer comes with the formula, the substitution and a picture — exactly how CBSE and State board answers are expected to be written.

    Pick a shape

    Switch between 2D shapes and 3D solids, then tap the shape you need.

    Type the measurements

    Enter radius, sides, height or diagonals. The diagram redraws with your values.

    Choose π and unit

    Use 22/7, 3.14 or keep the answer in terms of π, in cm, m, inches and more.

    Copy the working

    Follow the numbered steps, copy the answer or download the diagram for notes.

    Perimeter vs area

    Perimeter is the length of the boundary (unit: cm). Area is the region covered (unit: cm²).

    Rectangle 8 cm × 5 cm → P = 2(8 + 5) = 26 cm, A = 8 × 5 = 40 cm².

    CSA, TSA and volume

    CSA (curved / lateral surface area) leaves out the top and bottom. TSA adds them back. Volume is the space inside, in cubic units.

    Cylinder: CSA = 2πrh, TSA = 2πr(r + h), V = πr²h.

    Heron’s formula

    When you know all three sides of a triangle but not its height:

    s = (a + b + c) ÷ 2, A = √(s(s−a)(s−b)(s−c))

    Sides 13, 14, 15 → s = 21 → A = √(21×8×7×6) = 84 square units.

    Volume and capacity

    1 litre = 1000 cm³ and 1 m³ = 1000 litres. A tank of 2 m × 1.5 m × 1 m holds 3 m³ = 3000 L of water.

    Cone slant height: l = √(r² + h²)

    Exam tip: Use π = 22/7 when the radius or diameter is a multiple of 7 — the 7 cancels and your answer stays a neat whole number. Otherwise use 3.14, or leave the answer in terms of π if the question says so.
    Questions & answers

    Geometry Shape Calculator — your questions

    What is the difference between area and perimeter?

    Perimeter is the distance all the way round the boundary of a shape, measured in units of length such as cm. Area is the amount of surface the shape covers, measured in square units such as cm². A rectangle 8 cm by 5 cm has a perimeter of 26 cm and an area of 40 cm².

    What is Heron's formula?

    Heron's formula finds the area of a triangle from its three sides alone, with no height needed. First find the semi-perimeter s = (a + b + c) ÷ 2, then Area = √(s(s − a)(s − b)(s − c)). For sides 13, 14 and 15, s = 21 and the area is √(21 × 8 × 7 × 6) = 84 square units.

    What is the difference between CSA and TSA?

    Curved or lateral surface area covers only the curved or side faces, while total surface area adds the flat ends as well. For a cylinder, CSA = 2πrh and TSA = 2πr(r + h). A closed tin needs the TSA; a label wrapped round the tin only needs the CSA.

    When should I use 22/7 and when 3.14 for pi?

    Use 22/7 when the radius or diameter is a multiple of 7, because the 7 cancels and leaves a neat answer. Use 3.14 otherwise, or leave the answer in terms of π if the question says so. Follow whichever value the question specifies, since examiners mark on that.

    How do I convert volume into litres?

    One litre equals 1000 cm³, and one cubic metre equals 1000 litres. So a tank measuring 2 m by 1.5 m by 1 m has a volume of 3 m³, which is 3000 litres. Always convert every measurement to the same unit before multiplying, or the answer will be wrong by a factor of a thousand.

    What is the slant height of a cone?

    The slant height l is the distance from the tip down the sloping side to the edge of the base, and it is found with l = √(r² + h²) because the radius, height and slant height form a right triangle. For r = 3 cm and h = 4 cm, l = 5 cm. CSA = πrl uses the slant height, not the vertical height.

    Which shapes does this calculator cover?

    It covers 21 shapes in all. The 13 plane shapes are circle, semicircle, sector, square, rectangle, triangle by base and height, triangle by three sides using Heron, equilateral triangle, right triangle, parallelogram, rhombus, trapezium and regular polygon. The 8 solids are cube, cuboid, cylinder, hollow cylinder, cone, sphere, hemisphere and frustum of a cone.