This calculator finds the volume of a right circular cylinder when you know the radius of the circular base and the perpendicular height (or length along the axis). Enter both measurements using the same unit (for example centimetres, metres, or inches); the volume is returned in the matching cubic unit. It uses the standard solid-geometry formula V = π r² h and is ideal for checking homework, revision, and quick classroom estimates.
Distance from the centre of the circular base to its edge; same unit as height.
Perpendicular distance between the two circular bases (axis length); same unit as radius.
This calculator finds the volume of a right circular cylinder when you know the radius of the circular base and the perpendicular height (or length along the axis). Enter both measurements using the same unit (for example centimetres, metres, or inches); the volume is returned in the matching cubic unit. It uses the standard solid-geometry formula V = π r² h and is ideal for checking homework, revision, and quick classroom estimates.
For a right circular cylinder with base radius r and height h: V = π r² h where V is the volume of the solid. The same formula applies when h is the length of the cylinder along its axis.
If the radius r = 3 cm and the height h = 10 cm, then V = π × 3² × 10 = 90π ≈ 282.74 cm³. Multiplying by 3.14159 gives about 282.74 cubic centimetres.
It uses V = π r² h for a right circular cylinder, where r is the radius of the base and h is the height along the axis.
You can use any consistent length unit. If radius and height are both in inches, the volume is in cubic inches; if both are in metres, the volume is in cubic metres.
Divide the diameter by 2 to get the radius, then enter that value in the radius field.
This tool applies the cylinder geometry formula to your dimensions. A volume converter switches between units for a volume you already know; together they cover sizing the shape and expressing the result in another system if needed.
Cylinder Volume Calculator: Formula, Examples, and Homework Tips
A right circular cylinder is one of the most common solids in school geometry and in everyday objects such as cans, pipes, and columns. Its volume tells you how much space fits inside the circular ends and the straight sides. This short guide explains the standard formula, walks through a concrete example, and shows how the companion calculator on ProMathTools lets you check your own numbers quickly.
The volume of a right circular cylinder measures the three-dimensional space enclosed by two parallel congruent circles and the curved surface joining them. Mathematically, every cross-section parallel to the base is a circle with the same radius r, and the solid extends a perpendicular distance h along the axis. Multiplying the area of the circular base (π r²) by that height h gives the total volume. The reasoning is the same as stacking many thin circular slices: each slice has area π r², and h layers fill the cylinder. This model stays within the ideal solid taught in most US and UK curricula and does not try to model hollow walls, tapering, or non-circular bases.
V = π r² h, where r is the radius of the circular base and h is the perpendicular distance between the bases (the height). If you know the diameter d instead, use r = d / 2 first.
Suppose a soup can is modelled as a cylinder with radius 3 cm and height 10 cm. Then V = π × 3² × 10 = 90π. Using π ≈ 3.14159, the volume is about 282.74 cm³. If you measured in inches instead, the same arithmetic would give cubic inches — the unit follows whatever consistent lengths you typed in.
Open the cylinder volume tool and type the radius of the base in the first box and the height (axis length) in the second, using the same unit throughout. Press calculate to see the intermediate expression and the numeric volume. Read the last line as a cubic value in that unit system; compare with your written working to catch arithmetic slips or unit mix-ups.
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