Math
Sphere Calculator
A sphere is fixed by its radius, so the sphere calculator needs only one measurement: radius, diameter, circumference, surface area, or volume.
It solves for the radius first, then reports every other property exactly in terms of π and as a decimal, plus the capacity in liters and gallons for real units.
Surface area in square units, volume in cubic units, the rest are lengths.
Pick the unit your measurements use. Area is reported in square units and volume in cubic units.
Try an example
Result
Volume
—
- Volume (exact)
- —
- Surface area
- —
- Radius
- —
- Diameter
- —
- Circumference
- —
- Great-circle (cross-section) area
- —
More details (1 more)
- Capacity
- —
Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the sphere calculator solves
A sphere is fixed by its radius, so the sphere calculator needs only one measurement: radius, diameter, circumference, surface area, or volume. It solves for the radius first, then reports every other property exactly in terms of π and as a decimal, plus the capacity in liters and gallons for real units.
Formula
How to use it
- Choose the sphere measurement you know and enter it.
- Pick a unit so surface area and volume get the right labels and the volume converts to liters.
- Read the radius, diameter, circumference, surface area, volume, and great-circle area.
How to read the answer
Every result comes from the radius. Surface area grows with r² and volume with r³, so doubling the radius makes the surface 4 times larger and the volume 8 times larger. The great circle is the biggest circle you can slice through the center; its area is πr² and its circumference is the sphere's circumference.
Common mistakes and edge cases
- Using the diameter in (4/3)πr³ — that makes the volume 8 times too big. Halve it first or choose the diameter mode.
- Mixing up surface area (4πr²) with the cross-section area (πr²). The surface is exactly 4 great circles.
- Taking a square root instead of a cube root when solving for the radius from volume.
- Zero or negative measurements cannot form a sphere.
Worked examples
Radius 3 (volume 36π, surface 36π)
Volume
113.0973
Diameter 10 in
Volume
523.5988
Surface area 100 square units
Volume
94.0316
Volume 500 ft³ → radius
Volume
500
Circumference 31.4159 (radius ≈ 5)
Volume
523.5974
Decimal radius 2.5
Volume
65.4498
Zero radius (impossible)
Volume
Error
Frequently asked questions
What is the volume of a sphere?+
V = (4/3)πr³. A sphere with radius 3 has volume 36π ≈ 113.10 cubic units.
What is the surface area of a sphere?+
SA = 4πr² — four times the area of its great circle. Radius 3 gives 36π ≈ 113.10 square units (the same number as the volume only at r = 3).
How do I find the radius of a sphere from its volume?+
r = cbrt(3V / (4π)). A volume of 500 gives r ≈ 4.924.
How do I find the radius from the surface area?+
r = sqrt(SA / (4π)). Surface area 100 gives r ≈ 2.821.
How does the sphere formula relate to the cylinder?+
Archimedes showed a sphere fills exactly 2/3 of the cylinder that just contains it (radius r, height 2r), which has volume 2πr³. Two thirds of that is (4/3)πr³.
What is a great circle?+
The largest circle on a sphere, made by slicing through the center. Its circumference 2πr is what people mean by the sphere's circumference, and its area is πr².
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026