Volume Calculator
Volume and surface area of a cube, cuboid, cylinder, sphere, cone or square pyramid: enter the dimensions and read the result with the volume formula.
Result
---
Note: These calculations are for informational purposes only and do not replace professional tax or financial advice. All information without guarantee.
FAQ
Frequently Asked Questions
How do I calculate the volume of common shapes?
Cube: side cubed. Cuboid: length times width times height. Sphere: 4/3 times pi times radius cubed. Cylinder: pi times radius squared times height. Cone: 1/3 times pi times radius squared times height.
How do I convert between volume units?
One liter equals 1,000 cubic centimeters equals 0.001 cubic meters. One cubic meter equals 1,000 liters. One milliliter equals one cubic centimeter.
How does the calculator work out the surface area of a cone and a pyramid?
For both solids the calculator first derives the slant height from the radius or base side and the vertical height (Pythagorean theorem). Cone: s = √(r² + h²), surface area = π × r × (r + s); with r = 3 and h = 4, s = 5, the volume is 37.70 and the surface area 75.40. The pyramid is a right pyramid with a square base: h_s = √((a/2)² + h²), surface area = a² + 2 × a × h_s; with a = 6 and h = 4 you get h_s = 5, a volume of 48 and a surface area of 96. Always enter the vertical height as h, not the slant height.
Guide
What is the Volume Calculator?
The volume calculator computes the volume of geometric solids: cuboid, sphere, cylinder, cone, pyramid and more.
How does the Volume Calculator work?
Select the shape and enter the dimensions. The calculator computes the volume and shows the formula used. Conversion between cubic centimetres, litres and cubic metres is built in.
Key Data and Facts
Cuboid: V = a * b * c. Sphere: V = 4/3 * pi * r cubed. Cone: V = 1/3 * pi * r squared * h. Pyramid: V = 1/3 * base * h. 1 m cubed = 1,000 litres.
Step-by-Step Guide
How to calculate the volume of geometric bodies step by step: 1. Choose the shape of the body: cuboid, sphere, cylinder, cone, pyramid, prism or others. 2. Enter the dimensions: depending on the body, length, width, height, radius etc. 3. Volume formulas: cuboid: V = length x width x height. Cube: V = a3. Sphere: V = 4/3 x pi x r3. Cylinder: V = pi x r2 x h. Cone: V = 1/3 x pi x r2 x h. Pyramid: V = 1/3 x base area x height. Hemisphere: V = 2/3 x pi x r3. 4. Convert units: 1 m3 = 1,000 liters = 1,000,000 cm3. 1 cm3 = 1 ml. 5. Practical applications: amount of concrete for foundations (cuboid), tank capacity (cylinder), earth excavation (pyramid/cone). 6. For composite bodies: divide the body into simple basic shapes and add up the individual volumes.
Calculation Example
Cone with r = 6 cm, h = 15 cm: V = 1/3 x 3.14159 x 36 x 15 = 565.5 cm3 ≈ 0.566 liters. Sphere with r = 10 cm: V = 4/3 x 3.14159 x 1,000 = 4,189 cm3 ≈ 4.19 liters.
Sources
Official sources
Calculations are based on applicable German laws and official data:
Full methodology at Methodology.
Reviewed by Konstantin Iakovlev · Last updated:
Mathematics
Related Calculators
Percentage Calculator
What is X% of Y, what percentage is one value of another, and by how much did it change? The calculator shows the result and the formula with your numbers.
Rule of Three Calculator
Solve direct and inverse proportion problems: enter the known pair and the new value to get the result, a three-step solution and the formula used.
Fraction Calculator
Add, subtract, multiply or divide two fractions. The result is reduced to lowest terms automatically and is also shown as a decimal number.
Online Calculator
A browser calculator for the four basic operations, with a percent key, sign change, backspace and chained calculations across several steps.