Volume Calculator with Surface Area and Unit Conversion
Calculate the volume and available surface-area measures for ten common solids. Select the dimension unit and output unit independently, review the exact formula substitution, and use the live diagram to verify which measurements the selected shape requires.
Solid and dimensions
Volume and geometry results
Volume formulas for common solids
This volume calculator provides a dedicated calculation workflow rather than a generic converter. Volume measures three-dimensional capacity in cubic units. Surface area measures the exposed two-dimensional boundary, so its unit is squared rather than cubed.
Rectangular solids and cubes
A box uses length × width × height. A cube is the special case with all sides equal, giving volume s³ and total surface area 6s².
Circular solids
Cylinder volume is πr²h, cone volume is one third of that cylinder, and sphere volume is 4πr³/3. The calculator also reports total surface area where the necessary dimensions are available.
Capsules and hemispheres
A capsule combines a cylinder with two hemispherical ends, equal to one complete sphere. A hemisphere result includes both curved area and the circular base in its total surface area.
Prisms, pyramids and frustums
A triangular prism multiplies the triangular base area by prism length. A square pyramid uses one third of base area times vertical height. A conical frustum uses both end radii and the vertical height.
Unit conversion
The engine converts every entered length to meters, computes cubic meters and square meters, then converts to the selected volume display unit. Liters and U.S. gallons are capacity conversions from cubic meters.
Why are volume units cubed?
Volume combines three perpendicular dimensions, so the length unit is multiplied three times.
Can I mix inches and feet in one shape?
No. Select one input length unit and convert all dimensions to it before entry; this prevents silent mixed-unit errors.
Does surface area include bases?
The displayed total surface area includes closed bases for the supported solid definitions.