Numbers in, cubic result out
Open a shape tab. Fill every length the form asks for. The volume field updates on each keystroke. No submit button, no upload, no account.
Behind the tab, the page multiplies the measurements with the classical solid-geometry formula for the shape you picked. Rectangular prism multiplies three edges. Sphere uses four thirds pi r cubed. Cylinder multiplies base area by height. Cone and square pyramid each take one third of a prism-like solid with the same base and height.
Pi comes from the browser Math object, roughly sixteen digits of working precision. Display trims trailing noise so a homework answer stays readable. The substitution line under the result shows the numbers the formula used, so you spot a diameter slip without opening a second calculator.
Worked solids you already recognise
Shipping carton
Length 45 cm, width 30 cm, height 25 cm.
V = 45 × 30 × 25
V = 33750 cm³V = 33.75 litresUse Prism. Same arithmetic as packing foam volume for a warehouse pick list.
Playground ball
Diameter stamped 22 cm, so radius is 11 cm.
V = (4/3) × π × 11³V ≈ 5575.28 cm³Use Sphere with 11, never 22. Feeding 22 returns about 44,602 cm³, which is eight times too large.
Paint tin
Inner radius 8.5 cm, fill height 18 cm.
V = π × 8.5² × 18
V ≈ 4084.07 cm³V ≈ 4.08 litresUse Cylinder. A matching cone with the same base and height holds about 1.36 litres, one third of the tin.
Load any of the preset buttons above the inputs to drop these kinds of numbers into the form without typing. Then change one edge and watch the cubic value move.
Where the one-third factor comes from
A cone fits inside a cylinder of equal base and height. Stack three identical cones of fill material into the cylinder and the cylinder fills exactly. The same packing story holds for a pyramid inside a prism with matching base area and height. Textbooks write the factor as 1/3. Skip writing and you over-order material by a factor of three.
| Shape | Inputs on this page | Formula used |
|---|---|---|
| Rectangular prism | Length, width, height | V = lwh |
| Sphere | Radius | V = (4/3)πr³ |
| Cylinder | Radius, height | V = πr²h |
| Cone | Radius, height | V = (1/3)πr²h |
| Square pyramid | Base side, height | V = (1/3)a²h |
Height for a cone or pyramid is the perpendicular distance from the apex to the base plane. Slant height along the side face belongs in surface-area work, not here. Measuring along the slope and calling the number height inflates every cone and pyramid result.
What this calculator refuses to do
- No irregular solids. A rock, a bent pipe, or a vase with a curved profile needs water displacement or CAD, not five school formulas.
- No hollow shells. Outer dimensions alone ignore wall thickness. Subtract inner volume yourself, or model both surfaces.
- No unit conversion. Switching the label from cm to in renames the output. Convert inputs first with the length tools, or use the Volume Converter after you have a cubic number.
- Square pyramids only. A rectangular base needs base length times base width times height over three. That path lives closer to the Polyhedron Calculator.
- No surface area. Faces and wireframes belong on the polyhedron page. This page answers one question: how much space sits inside.
- Zero or blank fields yield a dash. Negative lengths never appear as volume. Empty inputs stay empty rather than printing zero as a fake answer.
Tips while you type
- Keep all three prism edges in the same unit before you multiply.
- For litres from cubic centimetres, divide by 1000. For cubic metres from centimetres, divide by 1,000,000.
- When packing foam quotes density in kg per cubic metre, convert your volume to m³ first or the mass comes out wrong by orders of magnitude.
- Need the floor footprint instead of fill capacity? Switch to the Area Calculator or the Circle Calculator for the base alone.
Formulas follow standard Euclidean solid geometry. Numbers stay in your browser tab. Nothing is stored on a server. Reviewed alongside the shape tabs whenever the page file changes.
