Result
Result reflects the current submitted inputs.
- Risk A
- Reviewed 2026-05-26
- 1 sources
- Inputs use one consistent linear unit.
- Volume is reported in cubic units.
- Intermediate values are not rounded.
- Box volume uses length x width x height.
Accuracy notes
- Risk level
- A
- Reviewed
- 2026-05-26
- Sources
- 1
- Primary result
- Volume
Formula logic is kept in a pure calculator module with fixtures, source notes, and page-visible assumptions.
What the result means
Volume is the space a 3D shape occupies, measured in cubic units. 1 liter = 1000 cm^3 = 0.001 m^3. 1 gallon (US) is about 3.785 liters.
Use the result this way
- Start with Volume, then use supporting outputs for context.
- Verify Shape, Length, and Width before copying the result.
- Check the formula, example, and assumptions before reusing the answer.
User job
How to use this calculator
Use Volume Calculator when you need volume for quick number work, classwork, spreadsheet checks, and explaining a calculation to someone else.
Best for
- Checking the core numeric relationship
- Comparing the main result with supporting outputs
- Reviewing a default example before entering your own shape and length.
Check before relying
- Confirm sign, decimal, percent, and rounding assumptions before copying the number.
- Inputs use one consistent linear unit.
- The cylinder is a right circular cylinder.
- Source context: OpenStax, reviewed 2026-06-18.
Next useful step
- Surface Area CalculatorUse next when your task shifts from Volume Calculator to Surface Area Calculator.
- Area CalculatorUse next when your task shifts from Volume Calculator to Area Calculator.
Formula
Cube: V = s^3. Box: V = length x width x height. Cylinder: V = pi x r^2 x h. Sphere: V = (4/3) x pi x r^3. Cone: V = (1/3) x pi x r^2 x h. Pyramid (rectangular base): V = (1/3) x length x width x height. Always cube the units (e.g., cm in -> cm^3 out).
- Cube: V = s^3 (side cubed). Rectangular prism: V = l x w x h.
- Cylinder: V = pi x r^2 x h. Sphere: V = (4/3) x pi x r^3. Cone: V = (1/3) x pi x r^2 x h (one third of the cylinder with the same base and height).
- Pyramid: V = (1/3) x base area x height. For a rectangular pyramid base, that is (1/3) x l x w x h.
- Common conversions: 1 m^3 = 1,000,000 cm^3 = 1,000 liters; 1 cubic foot = 7.481 US gallons.
- Volume scales with the cube of length: doubling every side multiplies volume by 8.
Inputs
Pick the shape, then enter the relevant dimensions (side, radius, height, etc.). Use consistent units; the result will be in those units cubed.
Example
A box 10 x 5 x 4 cm has volume 200 cm^3. A cylinder with radius 3 and height 7 has V = 3.14159 x 9 x 7 = about 197.92. A sphere with radius 5: V = (4/3) x 3.14159 x 125 = about 523.60.
FAQ
What is the volume formula?
It depends on the shape. Cube: s^3. Rectangular box: l x w x h. Cylinder: pi x r^2 x h. Sphere: (4/3) x pi x r^3. Cone and pyramid: (1/3) of the matching prism.
How do you calculate the volume of a cylinder?
Multiply pi (about 3.14159) by the radius squared by the height: V = pi x r^2 x h. A cylinder with r = 3 and h = 7 has V about 197.92.
How do you find the volume of a sphere?
V = (4/3) x pi x r^3. For r = 5, V = (4/3) x 3.14159 x 125, which is about 523.60 cubic units.
What units is volume measured in?
Cubic units of whatever length you used: cm^3, m^3, in^3, ft^3. 1 m^3 = 1000 liters = 1,000,000 cm^3; 1 ft^3 is about 7.481 US gallons.
How is a cone's volume related to a cylinder's?
A cone has exactly one third the volume of a cylinder with the same base and height. That's why the cone formula is (1/3) x pi x r^2 x h.
How do you find the volume of an irregular shape?
Split it into simple shapes (boxes, cylinders, etc.), calculate each, and add them up. Or use water displacement: submerge the object and measure the displaced liquid.
Sources
Last reviewed: 2026-05-26
- academicReviewed 2026-06-18Prealgebra 2e, Section 9.6: Solve Geometry Applications: Volume and Surface AreaOpenStax. Volume formulas for common 3D shapes.
Disclaimer
Results are theoretical volumes based on the entered dimensions. Real-world objects may have hollow interiors, irregularities, or material thickness that change the effective volume.