HOME / MATHEMATICS & STATISTICS / GEOMETRY / VOLUME OF A SPHERE CALCULATOR
Mathematics & Statistics / Geometry

Volume of a Sphere Calculator

I know the

Unit

Sphere

V=43πr3=500π3≈523.59878 cm3V = \tfrac{4}{3}\pi r^{3} = \frac{500\pi}{3} \approx 523.59878\,\text{cm}^{3}
A=4πr2=100π≈314.15927 cm2A = 4\pi r^{2} = 100\pi \approx 314.15927\,\text{cm}^{2}

Holds about 0.523599 L.

All measurements

Radius r
5 cm
Diameter d
10 cm
Circumference
31.415927 cm
Volume
523.59878 cm³
Surface area
314.15927 cm²

Doubling the radius multiplies the volume by 8 and the surface area by 4.

Find a sphere's volume, surface area, diameter and circumference from whichever one you know: radius, diameter, volume or surface area. Results come in your unit, with the volume also in liters.

Formula

V=(43)πr3\text{V} = (\frac{4}{3}) \pi \text{r}^{3}
A=4πr2\text{A} = 4 \pi \text{r}^{2}
r=3V/(4π)3\text{r} = \sqrt[3]{3\text{V} / (4 \pi )}

Worked Example

Radius5 cm
Result
Volume523.60 cm³ (0.524 L)
Surface area314.16 cm²

V = (4/3) × π × 5³ = 500π/3 ≈ 523.60 cm³ and A = 4 × π × 5² = 100π ≈ 314.16 cm². Since 1 L = 1,000 cm³, the sphere holds about half a liter.

Frequently Asked Questions

How do I find the radius from the volume?

Rearrange V = (4/3)πr³ to r = ∛(3V ÷ 4π). A 1-liter sphere (1,000 cm³) has a radius of ∛(3,000 ÷ 12.566) ≈ 6.20 cm.

What happens to the volume when the radius doubles?

It grows by a factor of 2³ = 8, while the surface area grows by 2² = 4. That is why large tanks hold much more for their surface, and why small droplets evaporate quickly.

How many liters is a cubic foot or a cubic meter?

1 m³ = 1,000 L and 1 ft³ ≈ 28.32 L. 1 in³ ≈ 16.39 mL.

Related Calculators

Circle Sector Area CalculatorConcrete Volume CalculatorUnit Converter (SI-Imperial)