Volume of a Hemisphere Calculator
Calculate the volume, curved surface area, total surface area, and circumference of a hemisphere from its radius. See also Volume of Sphere Calculator and Volume of Ellipsoid Calculator.
How to Calculate the Volume of a Hemisphere
A hemisphere is exactly half of a sphere. To find its volume, use the formula V = (2/3)πr³ — which is half the sphere volume formula. The curved surface area covers only the dome, while the total surface area includes the flat circular base. This calculator computes all values from the radius.
Hemisphere Volume Formula
V = (2/3) × π × r³
Curved Surface Area (CSA) = 2 × π × r²
Total Surface Area (TSA) = 3 × π × r²
Circumference = 2 × π × r
Base Area = π × r²
Example
Find the volume of a hemisphere with radius 5:
V = (2/3) × π × r³
V = (2/3) × π × 5³
V = (2/3) × π × 125
V ≈ 261.7994 cubic units
CSA = 2 × π × 25 ≈ 157.0796
TSA = 3 × π × 25 ≈ 235.6194
Hemisphere Volume Reference Table
| Radius | Volume | Curved SA | Total SA |
|---|---|---|---|
| 1 | 2.0944 | 6.2832 | 9.4248 |
| 2 | 16.7552 | 25.1327 | 37.6991 |
| 3 | 56.5487 | 56.5487 | 84.8230 |
| 4 | 134.0413 | 100.5310 | 150.7964 |
| 5 | 261.7994 | 157.0796 | 235.6194 |
| 6 | 452.3893 | 226.1947 | 339.2920 |
| 7 | 718.3775 | 307.8761 | 461.8141 |
| 8 | 1072.3303 | 402.1239 | 603.1858 |
| 9 | 1526.8140 | 508.9380 | 763.4070 |
| 10 | 2094.3951 | 628.3185 | 942.4778 |
| 15 | 7068.5835 | 1413.7167 | 2120.5750 |
| 20 | 16755.1608 | 2513.2741 | 3769.9112 |
| 25 | 32724.9235 | 3926.9908 | 5890.4862 |
| 50 | 261799.3878 | 15707.9633 | 23561.9449 |
| 100 | 2094395.1024 | 62831.8531 | 94247.7796 |
Frequently Asked Questions
What is a hemisphere?
A hemisphere is exactly half of a sphere, cut along a great circle. It has a curved dome surface and a flat circular base. A bowl is a common real-world example of a hemisphere shape.
What is the difference between curved and total surface area?
The curved surface area (CSA = 2πr²) covers only the dome. The total surface area (TSA = 3πr²) adds the flat circular base (πr²). Use TSA when the base is part of the surface, and CSA when only the dome matters.
How does hemisphere volume relate to sphere volume?
The hemisphere volume is exactly half the sphere volume. Sphere V = (4/3)πr³, so hemisphere V = (2/3)πr³. Two hemispheres of the same radius make one complete sphere.
How do I find the radius from the volume?
Rearrange the formula: r = ∛(3V / (2π)). For example, if V = 261.8, then r = ∛(785.4 / 6.2832) = ∛125 = 5.