Volume Calculator
0 cubic units
| Unit | Equivalent Volume |
|---|---|
| Cubic units (input scale) | |
| Liters (if units = cm) | |
| US Gallons (if units = inches) |
How Volume Is Calculated for Each Shape
Volume measures how much three-dimensional space a solid occupies, expressed in cubic units. Each shape has its own well-established formula: a rectangular box is length × width × height; a cube is side³; a sphere is (4/3)πr³; a cylinder is πr²h; a cone is (1/3)πr²h; a rectangular pyramid is (1/3) × base area × height; and a capsule (a cylinder capped with two hemispheres) is the cylinder's volume plus a full sphere's volume, (4/3)πr³ + πr²h. This calculator also reports the total surface area for each shape, since the two figures are often needed together for material or capacity planning.
Keep Your Units Consistent
All dimensions must be entered in the same unit (all inches, all centimeters, all meters, etc.) — the calculator has no way to know which unit you intended, so mixing units silently produces a meaningless result. The output is always in cubic units of whatever you entered; the conversion rows are only meaningful if you actually entered centimeters or inches as noted. For converting between differently-shaped 2D regions instead, see the area calculator, and for a deeper look at circular and spherical measurements use the circle calculator.
A Common Mistake: Radius vs. Diameter
Every sphere, cylinder, and cone formula here uses radius, not diameter — plugging in a diameter by mistake overstates the volume by a factor of 8 for a sphere (since radius is cubed) or 4 for a cylinder or cone (since radius is squared). If you only know the diameter, halve it first. For solids built from straight edges rather than curves, the surface area calculator covers the related 2D-surface side of the same shapes.
Frequently Asked Questions
Do all dimensions need to be in the same unit?
Yes. The calculator has no unit awareness - if you enter length in inches and height in centimeters, the result is meaningless. Enter every dimension for a given shape in the same unit, and the volume/surface area will come out in that unit cubed/squared. Use the conversion rows only if you actually entered centimeters or inches, as noted.
What is a capsule shape and how is its volume calculated?
A capsule is a cylinder with a hemisphere capping each flat end (think of a pill or a rounded fuel tank). Its volume is the cylinder's volume (pi r squared h, using only the straight middle section's height) plus a full sphere's volume (4/3 pi r cubed) formed by combining the two hemispherical caps, since two hemispheres of the same radius make one complete sphere.