Hemisphere Volume Calculator

Enter the radius of a hemisphere — half a sphere — to get its volume, curved area and total surface area, drawn to scale. Click the diameter on the drawing to change it.

Dimensions

Hemisphere
Blueprint · Isometric Click an amber dimension to edit it · isometric, not to printed scale

Result

Volume of a hemisphere

A hemisphere is a sphere cut in half through its centre, leaving a domed top on a flat circular base. Its volume is half a sphere's, ⅔πr³, and its total surface adds the flat base to the curved dome.

Editing on the drawing

Click the diameter on the figure and type a new value — the radius is set to half and the dome redraws to scale.

How to find the volume of a hemisphere

A hemisphere is exactly half a sphere, cut through the centre. It has a curved dome and a flat circular base, and a single measurement — the radius — describes it.

The formulas

The volume is half a sphere's. The curved area is also half a sphere's; adding the flat circular base gives the total surface area.

V = ⅔πr³
A = 2πr² + πr² = 3πr²

Worked example

Take a hemisphere of radius 52.

Step 1 — volume

Half a sphere's volume.

V = ⅔ × π × 52³ = ⅔ × π × 140,608 ≈ 294,489
Step 2 — curved area

Half a sphere's surface.

2πr² = 2π × 52² ≈ 16,990
Step 3 — total surface area

Dome plus the flat base.

A = 3π × 52² ≈ 25,485

What else the calculator returns

You get the curved area and the flat base area separately as well as the total, plus the diameter. Decide which surface you need: a solid dome's outer skin is the curved area, while a closed half-shell adds the base.

Where it comes up

Hemisphere volumes describe domes and cupolas, bowls, the rounded ends of tanks and pressure vessels, and half-round mouldings.

Frequently asked questions

How do you find the volume of a hemisphere?

Take half a sphere's volume: V = ⅔πr³.

What is the difference between curved and total surface area?

The curved area is the dome alone, 2πr². The total surface area adds the flat circular base, πr², giving 3πr².

Is a hemisphere's volume half a sphere's?

Yes, exactly half: ⅔πr³ against the sphere's 4⁄3πr³.

How do I find the radius from the volume?

Rearrange the formula: r = ∛(3V / 2π).

Is a dome the same as a hemisphere?

Only when the dome is exactly half a sphere. Shallower or taller domes are spherical caps and use a different formula.