What is the formula for the volume of a hemisphere?

V = (2/3)πr³, where r is the radius. This is exactly half the volume of a full sphere (4/3)πr³.

Why is the volume of a hemisphere 2/3 πr³?

A sphere has volume (4/3)πr³. A hemisphere is exactly half a sphere, so its volume is half of that: (1/2) x (4/3)πr³ = (2/3)πr³.

How do I find the volume of a hemisphere from the diameter?

Divide the diameter by 2 to get the radius (r = d/2), then apply V = (2/3)π(d/2)³ = πd³/12. For example, d = 10 gives V ≈ 261.80 cubic units.

Does the calculator include the flat circular base?

The volume formula (2/3)πr³ gives the total enclosed volume of the hemisphere, which includes the space bounded by both the curved surface and the flat circular base.

What is the difference between radius and diameter?

The radius is the distance from the center of the base circle to its edge. The diameter is twice the radius. Enter only the radius in this calculator.

How accurate is the result?

The calculator uses JavaScript's built-in Math.PI constant (15+ significant digits) and displays results rounded to 6 significant figures to avoid misleading precision.

Volume of a Hemisphere Calculator

Name: Volume of a Hemisphere Calculator
Availability: InStock
Author: Nham Vu

Enter a radius to instantly calculate the volume of a hemisphere using the formula (2/3)πr³.

Hemisphere Radius

Radius

Formula

V = (2/3) × π × r³

where r is the radius of the hemisphere

Enter a radius to calculate the hemisphere volume

Summary