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Math • Hemisphere Volume Calculator

Hemisphere Volume Calculator

Calculate the volume and surface area of a hemisphere (half sphere) from its radius.

Volume (V = ⅔πr³)
261.799
Total Surface Area
235.619
Curved Surface Only
157.080
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Calculation Guide & Reference

Hemisphere Volume & Surface Area Mathematics

Hemisphere volume calculator computes the volume and surface area of a half-sphere from its radius, using V = (2/3)πr³.

Standardized Mathematical Formula
V = (2/3)πr³ | Total Surface Area = 3πr²

A hemisphere is exactly half of a sphere, so its volume is half of the sphere volume formula. Its total surface area includes both the curved half-sphere surface (2πr²) and the flat circular base (πr²).

Variables:
r:Radius of the hemisphere
How It Works (Step-by-Step)
  • 1Enter the radius of the hemisphere.
  • 2View the volume, total surface area, and curved-surface-only area.
Real-World Numerical Example
A Hemisphere with Radius 5

A half-sphere dome has a radius of 5 units.

•Volume: (2/3) × π × 5³ = (2/3) × π × 125 ≈ 261.80 cubic units.
•Total surface area: 3 × π × 5² ≈ 235.62 square units.
•Curved surface only: 2 × π × 5² ≈ 157.08 square units.
Result: The hemisphere has a volume of approximately 261.80 cubic units and a total surface area of about 235.62 square units.
Calculation Best Practices & Tips
Examine the discriminant (b² - 4ac) before solving quadratics to instantly know if roots are real, distinct, repeated, or complex.
In statistical analysis, always check both the mean and median to identify if data distribution is skewed by outliers.
When calculating percentage changes, ensure you divide by the original starting baseline value: ((New - Old) / Old) * 100.

Frequently Asked Questions (FAQ)

V = (2/3)πr³ — exactly half of the full sphere volume formula (4/3)πr³, since a hemisphere is half a sphere.

Because a hemisphere has an additional flat circular face (the "cut" base) that a full sphere doesn't have — half the curved surface (2πr²) plus that flat base (πr²) gives 3πr² total, not 2πr².

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