Circle Volume Formula Calculator

This calculator works out the volume of a sphere (often called a circle in 3D) from its radius, diameter, or circumference. You enter one of those measurements, and you get the volume in cubic units, plus the surface area for reference. The first result is the volume, which is what the page title asks for.

Formula

The volume of a sphere is given by the standard formula:

V = (4/3) π r³

Where:

• V is the volume (cubic meters, cubic feet, etc.)
• r is the radius (meters, feet, etc.)
• Ï€ (pi) is approximately 3.14159

If you only know the diameter (d), use r = d/2. If you only know the circumference (C), use r = C/(2Ï€). The calculator above does these conversions for you.

Worked Example

Using the default values from the calculator: radius = 1 m, diameter = 2 m, circumference ≈ 6.2832 m.

1. Start with the radius: r = 1 m.
2. Cube the radius: r³ = 1 m³.
3. Multiply by π: 1 × 3.14159 = 3.14159.
4. Multiply by 4/3: (4/3) × 3.14159 = 4.18879.

So the volume is 4.1888 m³ (rounded to 4 decimal places), matching the calculator output. The surface area is 4πr² = 4 × 3.14159 × 1 = 12.5664 m².

When to Use This Calculator

This is for spheres—perfectly round 3D objects like balls, planets, or bubbles. If you mean a flat circle, it has no volume; you might want the area (πr²) instead. Use this calculator when you need to know how much space a spherical object occupies, such as the capacity of a spherical tank, the volume of a ball bearing, or the amount of material in a spherical mold.

How to Read the Result

The volume is in cubic units, matching the unit you entered. If you enter meters, you get cubic meters (m³). If you enter feet, you get cubic feet (ft³). To convert to liters, multiply cubic meters by 1000. For gallons (US), multiply cubic meters by 264.172. The surface area is in square units (m² or ft²).

Common Mistakes and Misconceptions

• Confusing radius and diameter: A common error is using the diameter as the radius. The radius is half the diameter. If you enter the diameter directly, the calculator handles it, but if you do it manually, remember r = d/2.
• Unit mix-ups: If you measure in centimeters, the volume will be in cubic centimeters. To get liters, divide by 1000 (since 1 L = 1000 cm³). Don’t mix units—always convert to the same unit first.
• Using the circle area formula: A flat circle has area Ï€r², not volume. Some people mistakenly use Ï€r² for a sphere’s volume, which gives a much smaller number.
• Rounding too early: If you round Ï€ to 3.14, the result is slightly off. Use at least 3.14159 for accuracy.

Limits of the Formula

The formula assumes a perfect sphere with a uniform radius. Real objects are rarely perfect, so the result is an approximation. For example, the Earth is an oblate spheroid (slightly flattened at the poles), so its true volume is about 0.3% less than a perfect sphere of the same equatorial radius. The formula also assumes the object is solid; for a hollow sphere, you’d need to subtract the inner volume.

Alternatives and Related Calculations

If you have a different shape, here are common alternatives:

• Circle area: A = Ï€r² for a flat circle.
• Sphere surface area: A = 4Ï€r² (included in the calculator).
• Cylinder volume: V = Ï€r²h (for a can or pipe).
• Cone volume: V = (1/3)Ï€r²h.
• Ellipsoid volume: V = (4/3)Ï€abc, where a, b, c are the semi-axes.

For a sphere, you can also compute the volume from the diameter directly: V = (π/6)d³. This is sometimes easier when you measure across the widest point.

Frequently Asked Questions

What is the volume of a circle with radius 5 cm?

Using the formula V = (4/3)Ï€r³, with r = 5 cm: V = (4/3) × 3.14159 × 125 = 523.6 cm³. That’s about 0.524 liters.

How do I find the volume of a sphere from its circumference?

First find the radius: r = C/(2π). Then use the volume formula. For example, if C = 31.4 cm, then r = 31.4/(2×3.14159) = 5 cm, and V ≈ 523.6 cm³.

Is the volume of a sphere the same as the volume of a circle?

No. A circle is a 2D shape and has no volume, only area. A sphere is the 3D version. The page title says “circle volume” because people often say “circle” when they mean “sphere” in everyday language.

What is the volume of a sphere with diameter 10 inches?

Radius = 5 inches. V = (4/3)π(5³) = (4/3) × 3.14159 × 125 = 523.6 cubic inches. To convert to gallons, divide by 231 (since 1 US gallon = 231 in³), giving about 2.27 gallons.

Why does the calculator show surface area too?

Surface area is often needed alongside volume, for example to estimate material needed to cover a sphere or heat transfer. It’s a useful bonus, but the volume is the primary result.

Related

• Area Calculator Triangle: How to Find It Fast
• Area Calculator Soft: What It Means & How to Use
• Area Calculator m2: How to Measure Square Meters

in r | Radius | m | 1 | 0
in d | Diameter | m | 2 | 0
in c | Circumference | m | 6.2832 | 0
out V | Volume | m^3 | (4/3) * pi * r^3 | 4
out A | Surface area | m^2 | 4 * pi * r^2 | 4