Volume Calculator
Volume of 14 solids with steps and diagrams, in litres, m³, ft³ or gallons, plus weight.
Result
This is the last result worked out. Fix the input above to update it.
Step by step
Volume in other units
| Unit | Volume |
|---|
Weight in other units
| Unit | Mass |
|---|
About the Volume Calculator
Pick a solid, type its sizes, and get its volume with the formula and every step, a labelled diagram, and the result in m³, litres, cm³, cubic feet and inches, cubic yards, and US and imperial gallons. Fourteen solids are covered: cube, cuboid, cylinder, hollow cylinder or pipe (from radii, diameters or the wall thickness, with what it holds), cone and frustum (from the height or the slant height), sphere, hemisphere, spherical cap or dome, pyramid (square, rectangular, regular-polygon or any base), prism (triangular, regular-polygon or any base), capsule, ellipsoid and torus.
With whole-number or fractional sizes the answer is also given exactly in terms of π — 490π cm³ for a cylinder of radius 7 and height 10 — and π can be set to 22/7 or 3.14 to match a textbook. Choose a material, or type a density, to get the weight of the solid as well.
How to use it
- Choose the solid and the unit your sizes are in.
- Type the sizes shown on the diagram. Where it helps, pick what you know — radius or diameter, height or slant height, outer diameter and wall thickness for a pipe.
- Read the volume, its exact form in terms of π, and the litres; the steps show the formula with your numbers and the table converts to other units.
- For the weight, choose a material or “Other” and type its density in kg/m³, g/cm³ or lb/ft³. Copy or download the full working.
Examples
r = 7 cm, h = 10 cm
V = 1540 cm³ = 1.54 L
V = πr²h = (22/7) × 49 × 10. With π itself, 490π ≈ 1539.38 cm³.
r = 3 cm, h = 4 cm
V = 12π ≈ 37.6991 cm³
V = ⅓πr²h = ⅓ × π × 9 × 4. The slant height is √(9 + 16) = 5 cm.
R = 8, r = 4, h = 3
V = 112π ≈ 351.8584
V = ⅓πh(R² + Rr + r²) = ⅓ × π × 3 × (64 + 32 + 16).
inner diameter 10 cm, length 2 m (200 cm)
holds 15.708 L
Capacity = πr²h = π × 5² × 200 = 15 707.96 cm³.
base radius a = 4, height h = 2
V = 52π/3 ≈ 54.4543
The sphere’s radius is (a² + h²)/(2h) = 5, and V = ⅓πh²(3r − h).
diameter 10 cm, steel 7850 kg/m³
≈ 4.11 kg
V = ⁴⁄₃π × 5³ ≈ 523.6 cm³ = 0.0005236 m³, and 0.0005236 × 7850 ≈ 4.110 kg.
Common uses
- Checking NCERT Class 9 and 10 “Surface Areas and Volumes” exercises, with π = 22/7 when the question says so.
- Working out how many litres a tank, drum, pipe or bottle holds.
- Estimating the weight of concrete, steel or other material from its dimensions.
- Converting a volume between m³, litres, cubic feet and gallons for orders and shipping.
The formulas
- Cube V = a³; cuboid V = l × b × h.
- Cylinder V = πr²h; hollow cylinder V = π(R² − r²)h (and it holds πr²h).
- Cone V = ⅓πr²h; frustum V = ⅓πh(R² + Rr + r²).
- Sphere V = ⁴⁄₃πr³; hemisphere V = ⅔πr³; spherical cap V = ⅓πh²(3r − h) = ⅙πh(3a² + h²).
- Pyramid V = ⅓ × base area × height; prism V = base area × length — for any base shape.
- Capsule V = πr²L + ⁴⁄₃πr³ (a cylinder plus two hemispheres).
- Ellipsoid V = ⁴⁄₃πabc; torus V = 2π²Rr² (Pappus’s theorem: the tube’s cross-section πr² times the distance 2πR its centre travels).
Litres, gallons and cubic feet
One litre is 1000 cm³, so 1 m³ = 1000 L. The conversions use exact definitions (NIST SP 811): 1 US gallon = 231 cubic inches = 3.785411784 L, 1 imperial (UK) gallon = 4.54609 L, and 1 cubic foot = 28.316846592 L. A cubic metre is therefore about 264.17 US gallons, 219.97 imperial gallons and 35.31 cubic feet.
Weight from volume
Mass = density × volume. Water is very close to 1000 kg/m³, so a litre of water weighs about a kilogram. The material list uses typical values — structural steel 7850 kg/m³, plain concrete about 2400 kg/m³, pure aluminium 2700 kg/m³, copper 8960 kg/m³ — but real materials vary with their mix, alloy and temperature, so type the density from your supplier’s data sheet when it matters.
Limitations
- Sizes describe ideal solids. Real tanks have wall thickness, rounded corners and fittings — use the inside sizes for what a container holds.
- The weight uses the density you choose; the preset values are typical, not certified.
- Results are rounded to the decimal places you choose, and the unit tables keep at least six significant digits (calculations carry about 15). Sizes must be positive and at most 10¹² in the chosen unit.
- A pyramid or prism known only by its base area gets a volume but no surface area — that needs the base shape.
Privacy
Everything happens in your browser. What you enter or open here is not uploaded or stored by MySmartCoPilot.
Frequently asked questions
How do I find the volume of a cylinder in litres?
Work out V = πr²h with the radius and height in centimetres, then divide by 1000: a cylinder of radius 7 cm and height 10 cm holds 490π ≈ 1539.38 cm³ ≈ 1.54 L. In metres, multiply the m³ by 1000 instead. The table under the result shows litres for any unit.
What is the difference between the volume of a pipe and its capacity?
The volume of a hollow cylinder is the material in its wall, π(R² − r²)h. Its capacity — how much water it holds — is the inside space, πr²h. The calculator shows both. For a pipe given by its outer diameter and wall thickness, the inner radius is half the outer diameter minus the thickness.
Why does a cone hold one third of a cylinder?
A cone and a cylinder with the same base and height satisfy V(cone) = ⅓πr²h and V(cylinder) = πr²h, so the cone has exactly one third of the volume. The same ⅓ appears for every pyramid compared with the prism on the same base; it follows from Cavalieri’s principle or from integration.
Should I use π = 22/7?
Use it when your question says so — many NCERT problems do, and radii that are multiples of 7 then give whole-number answers (r = 7, h = 10 gives exactly 1540 cm³). The exact answer in terms of π, such as 490π cm³, is shown either way, and π itself is the right choice for real measurements.
How do I calculate the weight of an object from its volume?
Multiply the volume in m³ by the density in kg/m³. A steel ball 10 cm across has a volume of about 0.0005236 m³; at 7850 kg/m³ it weighs about 4.11 kg. Choose the material under “Weight of the solid”, or “Other” to type your own density.
What volume does a spherical cap or dome have?
For a cap of height h cut from a sphere of radius r, V = ⅓πh²(3r − h). If you know the radius a of its circular base instead, the sphere’s radius is r = (a² + h²)/(2h); a dome with a = 4 m and h = 2 m comes from a sphere of radius 5 m and holds 52π/3 ≈ 54.45 m³.