Volume Calculator
Volume and surface area of a box, cube, cylinder, sphere, cone or pyramid in any unit — cubic meters, liters, gallons, cubic feet — with the formula shown.
Volume Calculator: with the default inputs, volume is 3 m³.
Only the dimensions for the selected shape are used; the rest are ignored.
Perpendicular height from base to apex, not the slant.
Perpendicular height from base to apex.
- Surface area
- 13 m²
Assumptions
- Worked steps are shown in meters (the internal base unit); the result is converted to the unit you choose. Internally volume is carried in liters (1 m³ = 1,000 L).
- Pyramid means a right pyramid (apex above the centre of the rectangular base).
| Shape | Volume | Surface area |
|---|---|---|
| Box | length × width × height | 2(lw + lh + wh) |
| Cube | side³ | 6 × side² |
| Cylinder | π × r² × h | 2πr² + 2πrh |
| Sphere | 4⁄3 × π × r³ | 4πr² |
| Cone | π × r² × h ÷ 3 | πr² + πr × √(r² + h²) |
| Pyramid | base area × h ÷ 3 | base + 4 triangular faces |
Every cone or pyramid is exactly a third of the box or cylinder that contains it.
How this is worked out
The formula
Box V = l·w·h, S = 2(lw + lh + wh) Cube V = s³, S = 6s² Cylinder V = π r² h, S = 2πr² + 2πrh Sphere V = 4⁄3 π r³, S = 4πr² Cone V = ⅓ π r² h, S = πr² + πr·√(r² + h²) Rectangular pyramid V = ⅓ l·w·h, S = lw + l·√((w/2)² + h²) + w·√((l/2)² + h²) 1 m³ = 1,000 L = 264.17 US gal = 35.31 ft³
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- Shape
- Only the dimensions for the selected shape are used; the rest are ignored.Box (rectangular prism) · Cube · Cylinder · Sphere · Cone · Pyramid (rectangular base)
- Length
- A number.in mm, cm, m, in, ft, yd · 0 or more · defaults to 2
- Width
- A number.in mm, cm, m, in, ft, yd · 0 or more · defaults to 1.5
- Height
- A number.in mm, cm, m, in, ft, yd · 0 or more · defaults to 1
- Side
- A number.in mm, cm, m, in, ft, yd · 0 or more · defaults to 1
- Radius
- A number.in mm, cm, m, in, ft, yd · 0 or more · defaults to 0.5
- Height
- A number.in mm, cm, m, in, ft, yd · 0 or more · defaults to 2
- Radius
- A number.in mm, cm, m, in, ft, yd · 0 or more · defaults to 1
- Base radius
- A number.in mm, cm, m, in, ft, yd · 0 or more · defaults to 1
- Height
- Perpendicular height from base to apex, not the slant.in mm, cm, m, in, ft, yd · 0 or more · defaults to 3
- Base length
- A number.in mm, cm, m, in, ft, yd · 0 or more · defaults to 2
- Base width
- A number.in mm, cm, m, in, ft, yd · 0 or more · defaults to 2
- Height
- Perpendicular height from base to apex.in mm, cm, m, in, ft, yd · 0 or more · defaults to 3
What you get back
- Volumemain answer
- Surface area
What this assumes
- Worked steps are shown in meters (the internal base unit); the result is converted to the unit you choose. Internally volume is carried in liters (1 m³ = 1,000 L).
- Pyramid means a right pyramid (apex above the centre of the rectangular base).
About this calculator
Volume is the amount of space a solid takes up, measured in cubic units — or, for anything that holds liquid, in liters and gallons. This calculator gives the volume and the surface area of the six solids that cover almost every practical problem, from shipping boxes to water tanks to grain silos.
How to use it
Choose the shape and enter its dimensions in any length unit. The volume can be shown in cubic meters, liters, cubic feet, gallons and more, so "how many gallons does this cylindrical tank hold?" is a single calculation. Surface area is useful for paint, wrapping, sheet metal and heat loss.
Three ideas behind all the formulas
- Prisms and cylinders: base × height. A box is a stack of identical rectangles; a cylinder is a stack of identical circles. Volume = area of the base × how tall the stack is.
- Pointed solids are one third of the matching prism. A cone holds exactly a third of the cylinder with the same base and height; a pyramid holds a third of its box. You can verify it by pouring — three cones of water fill the cylinder.
- Spheres: 4⁄3 πr³. Archimedes showed a sphere is two-thirds of the cylinder that just contains it (radius r, height 2r), and he was proud enough to have it carved on his tomb.
Surface area
Surface area is the total area of the outside skin: unfold the solid into flat pieces and add them up. A cylinder unfolds into two circles and a rectangle whose width is the circumference; a cone into a circle and a sector whose slant edge is √(r² + h²).
Units
Cubic units scale by the cube of the length factor: 1 m³ = 1,000,000 cm³ = 1,000 L, and 1 yd³ = 27 ft³, not 3. That's why a "small" change in dimensions makes a big change in capacity — doubling a tank's radius quadruples its volume; doubling every dimension of a box makes it hold eight times as much.
Common mistakes
- Using diameter where the formula wants radius (this over-counts by 4×).
- Using the slant height of a cone or pyramid as its height. The volume formula wants the perpendicular height; the slant appears only in surface area.
- Converting cubic units by the linear factor.
Frequently asked questions
▸How do I find the volume of a cylinder?
Multiply the base area by the height: V = πr²h. A tank with radius 2 ft and height 5 ft holds π × 4 × 5 ≈ 62.8 ft³, about 470 US gallons.
▸How many liters are in a cubic meter?
Exactly 1,000. A liter is a cube 10 cm on a side, and 10 × 10 × 10 of them fill a cubic meter.
▸Why is a cone's volume one third of a cylinder's?
Because its cross-sections shrink to a point. Calculus makes it exact (integrating πr²(1 − z/h)² from 0 to h gives ⅓πr²h), but you can check it by filling a cone with water three times into a cylinder of the same base and height.
▸What's the difference between volume and surface area?
Volume is the space inside (cubic units, or liters/gallons); surface area is the total area of the outside faces (square units). A 1 m cube has volume 1 m³ and surface area 6 m².
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