1
Curved area, total area & volume
Radius or diameter in, all three measures out.
MATH TOOL
Hemisphere Calculator
A hemisphere is exactly half a sphere. Enter its radius or diameter and get the curved surface area, the total surface area (including the flat base), and the volume — every step shown.
Half a sphere, three useful measures
Slice a sphere through its center and you get a hemisphere: a dome with a flat circular base. Its measures all come from the full-sphere formulas, halved — except the total surface area, which adds the base back in. That base is the classic trap: the curved surface area is half the sphere's skin, but the total surface area includes the flat circle the hemisphere sits on.
A worked example
Take a hemisphere with radius r = 5 (say, inches). Curved surface area = 2πr² = 2 × π × 25 = 157.08. Base area = πr² = π × 25 = 78.54, so total surface = 157.08 + 78.54 = 235.62 (exactly 3πr²). Volume = ⅔πr³ = ⅔ × π × 125 = 261.80 cubic units. If you measured the diameter instead — say 10 — halve it first: r = 10 ÷ 2 = 5, then the same steps apply.
Output · formula · meaning
| Output | Formula | What it means |
|---|---|---|
| Curved surface area | 2πr² | Half the sphere's skin — the dome only, no base. |
| Base area | πr² | The flat circle the hemisphere sits on. |
| Total surface area | 3πr² | Curved + base — use this for paint or material on a closed dome. |
| Volume | ⅔πr³ | Half the sphere's volume — capacity of a hemispherical bowl. |
Who uses this
- Students: geometry homework on spheres and hemispheres — the curved-vs-total distinction is the question most textbooks actually test.
- Builders and makers: sizing a dome skylight, a pizza-oven dome, or a concrete half-sphere planter — surface area prices the material, volume prices the fill.
- Cooks and bakers: a hemispherical bowl's capacity in cups or liters follows straight from the volume formula.
- Science fair builders: estimating paint or resin for a model planet cut in half — a hemisphere is literally half a globe.
Accuracy & limitations
The formulas are exact geometry — results are accurate to the decimals shown. Two judgment calls: an open hemisphere (a bowl, no base) needs only the curved area, while a closed dome needs the total — pick the right one for your job. And if your "hemisphere" is squashed or stretched (an ellipsoid), these formulas under- or over-state the truth; this page assumes a true half-sphere.
Want the hand-worked version? The hemisphere area guide walks through the formulas step by step, and the math collection has more tools for everyday numbers.
Cite this calculatorBright Side Kit. “Hemisphere Calculator.” brightoolbox.com, 2026.
Bright Side Kit. "Hemisphere Calculator." https://brightoolbox.com/area-of-hemisphere-calculator/ Accessed October 22, 2026.Frequently asked questions
What is the formula for the surface area of a hemisphere?
The curved surface area is 2πr² — half a sphere's 4πr². The total surface area adds the flat circular base (πr²), giving 3πr². Use the curved value for an open dome and the total for a closed one.
How do you find the volume of a hemisphere?
Halve the sphere's volume: V = ⅔πr³. For r = 5, that's ⅔ × π × 125 = 261.80 cubic units — the calculator above shows every step.
Is the surface area of a hemisphere 2πr² or 3πr²?
Both — they measure different things. 2πr² is the curved dome only (an open bowl). 3πr² includes the flat base (a closed dome). This is the most common point of confusion, and the reason this calculator shows both.
How do I calculate hemisphere area from the diameter?
Halve the diameter to get the radius first: r = d ÷ 2. Then use the formulas above — for example, a 10-unit diameter gives r = 5, curved area 157.08, total area 235.62. Or just pick "Diameter" in the calculator above and it handles the halving.
What is a hemisphere in simple terms?
Exactly half of a sphere, cut through its center — think half an orange, a dome, or a bowl. It has one curved surface and one flat circular face.
How much paint do I need for a dome?
Work out the total surface area (3πr²) if the dome sits on a base you must paint too, or just the curved area (2πr²) if the base is hidden. Then check your paint can's coverage per square unit and divide.
What is the volume of a hemisphere with radius 5?
261.80 cubic units — ⅔ × π × 5³ = ⅔ × π × 125. That is half of a full sphere's 523.60.