R

Volume, Circle & Pythagoras Calculator

Volume in litres, surface area, circumference or hypotenuse: enter your measurements and get the result with a sketch, formula and step-by-step solution. For school, pools, tanks and rain barrels.

100% freeNo data storedStep-by-step solution

Choose a solid or shape

Solids (volume)

Shapes (area)

Enter measurements

cm
cm
Only need an area — rectangle, trapezoid, parallelogram or ellipse?Go to the area calculator
Cylinder · Volume

9,424.78 cm³

= 9.425 litres

Surface area

2,513.27 cm²

Weight when filled with water

9.425 kg

Sketch: Cylinder

r = 10 cmh = 30 cm

The sketch is simplified to scale; the labels show your values.

More measurements

Diameter d

20 cm

Base area B

314.16 cm²

Lateral area L

1,884.96 cm²

Formula & solution

  1. 1

    Base area

    G = π · r²
    G = π · 10² = 314.16 cm²
  2. 2

    Volume

    V = π · r² · h
    V = π · 10² · 30 = 314.16 · 30 = 9,424.78 cm³
  3. 3

    Lateral area

    M = 2 · π · r · h
    M = 2 · π · 10 · 30 = 1,884.96 cm²
  4. 4

    Surface area

    O = 2 · G + M
    O = 2 · 314.16 + 1,884.96 = 2,513.27 cm²
  5. 5

    Conversion to litres

    1 l = 1 dm³ = 1,000 cm³
    9,424.78 cm³ ÷ 1,000 = 9.425 l

Unit conversion

mm³9,424,777.96
cm³ (ml)9,424.78
dm³ (l)9.425
hl0.0942
m³0.009425

For comparison

≈ 6.283

1.5 l bottles

≈ 0.9425

10 l buckets

Email results

Was the volume calculator helpful?

Kaffee ausgeben ☕

Only need an area? Calculate rectangle, trapezoid or ellipse

Area Calculator →

Guide: Volume, Circles & Pythagoras

Formulas explained clearly, with worked examples from everyday life and school

How to Calculate Volume: Every Formula for Cube, Cylinder, Sphere, Cone & PyramidFeatured

How to Calculate Volume: Every Formula for Cube, Cylinder, Sphere, Cone & Pyramid

The complete guide to volume: formulas for all common solids, converting to litres, surface area, circles and the Pythagorean theorem — with step-by-step examples.

2026-09-249 min read
Pool Volume: How Many Litres Does Your Pool Hold?

Pool Volume: How Many Litres Does Your Pool Hold?

Rectangular pool, round pool or rain barrel: how to calculate the water volume in litres, plan the fill level and estimate water cost and weight realistically.

2026-09-246 min read
Circle Calculations: Circumference, Area, Radius and Diameter with Examples

Circle Calculations: Circumference, Area, Radius and Diameter with Examples

Every value from a single one: how to calculate circle area, circumference, radius and diameter — with formulas, working backwards and practical examples from flower beds to tree trunks.

2026-09-245 min read
Pythagorean Theorem: Formula, Examples and Finding Angles

Pythagorean Theorem: Formula, Examples and Finding Angles

a² + b² = c² explained clearly: find the hypotenuse and legs, work out diagonals, set out right angles and find angles with sine, cosine and tangent.

2026-09-245 min read
Converting Litres to Cubic Metres: m³, dm³, cm³ and ml Explained

Converting Litres to Cubic Metres: m³, dm³, cm³ and ml Explained

1 m³ = 1,000 litres, 1 cm³ = 1 ml: converting every volume unit with a table, rules of thumb for the weight of water and typical conversion mistakes.

2026-09-245 min read

You might also find useful

Area Calculator

Calculate area and perimeter: rectangle, circle, triangle, trapezoid and more

Calculate now →

Material Needs Calculator

Calculate tiles, paint, flooring & bulk materials

Calculate now →

Rule of Three Calculator

Proportional, inverse and compound rule of three with step-by-step solution

Calculate now →

Frequently Asked Questions

For solids with a constant cross-section (cube, cuboid, cylinder): volume = base area × height. For a cuboid that is length × width × height, for a cylinder π × r² × h. Pointed solids such as cones and pyramids have exactly one third of that volume. The sphere has its own formula: V = 4/3 × π × r³. Always convert all measurements to the same unit first.

One litre is exactly one cubic decimetre (1 l = 1 dm³). So 1 m³ = 1,000 l, 1 cm³ = 1 ml = 0.001 l and 1 mm³ = 0.000001 l. A pool of 48 m³ therefore holds 48,000 litres, a cylinder of 9,425 cm³ about 9.4 litres. The calculator shows the result in litres and all common units automatically.

The formula is V = π × r² × h. First calculate the circular base area π × r², then multiply by the height. If you only know the diameter, divide it by 2. Example: diameter 20 cm, height 30 cm gives r = 10 cm and V = π × 100 × 30 ≈ 9,425 cm³, about 9.4 litres.

The volume of a sphere is V = 4/3 × π × r³. The radius is cubed: if the radius doubles, the volume becomes eight times larger. A sphere with r = 1 has a volume of about 4.18879 cubic units, a sphere with r = 10 cm about 4,189 cm³ (roughly 4.2 litres). The surface area is A = 4 × π × r².

Circumference C = 2 × π × r = π × d, area A = π × r². Every other value can be derived from any single one: r = d ÷ 2, r = C ÷ (2π) or r = √(A ÷ π). In the calculator, choose "Circle" and select which value you know — radius, diameter, circumference or area.

In a right triangle, a² + b² = c². a and b are the legs at the right angle, c is the longest side, the hypotenuse. Example: a = 3 and b = 4 gives c = √(9 + 16) = 5. The angles follow from trigonometry: α = arctan(a ÷ b) ≈ 36.87° and β = 90° − α ≈ 53.13°. The calculator solves the triangle from any two known values.

A cone and a cylinder with the same base area and height differ in that the cone narrows evenly to its tip. Integrating the cross-sections gives exactly one third — hence V = 1/3 × π × r² × h. The same applies to a pyramid compared with a cuboid: V = 1/3 × a² × h. Put simply: three filled cones fill one cylinder.

Calculate rectangular pools as a cuboid (length × width × water depth) and round pools as a cylinder (π × r² × water depth). Use the actual fill level, not the wall height — usually 10 to 15 cm stay free. A pool of 8 × 4 m with 1.5 m water depth holds 48 m³ = 48,000 litres. Use the quick-start examples above and adjust the measurements.

Surface area is the entire outer skin of a solid: base, top and lateral surface together. Lateral area is only the "side wall" without base and top. For a cylinder: L = 2 × π × r × h, A = 2 × π × r² + L. This matters in practice for paint, liners or insulation: a pool liner needs the floor plus the lateral area, but no top.