Sphere Calculator
Calculate radius, diameter, surface area, and volume of a sphere from any one known measurement.
Did this tool work for you?
How to use this calculator
All sphere measurements derive from the radius. Enter any one known value — radius, diameter, surface area, or volume — and all others are computed.
- 1
Select the measurement you already know: radius, diameter, surface area, or volume.
- 2
Enter its value in the field below.
- 3
All other sphere measurements — radius, diameter, surface area, and volume — are calculated automatically.
Frequently asked questions
Which values can I start from?
Any one of radius, diameter, surface area or volume. The calculator converts it to a radius and derives the other three from that. Starting from a diameter of 26 gives a radius of 13, a surface area of 2123.716634 and a volume of 9202.77208.
How does it recover a radius from a surface area or volume?
Surface area 4πr² gives r = √(area ÷ 4π), and volume 4/3πr³ gives r = ∛(volume ÷ 4/3π). A surface area of 100 returns a radius of 2.820948, and a volume of 1000 returns 6.203505. The input you gave is reproduced exactly in the output, which makes a good check.
What is the “Great Circle Circumference”?
It is 2πr, the length of the largest circle you can draw on the sphere, such as the equator on a globe. For radius 6 it is 37.699112. It is not the sphere’s surface area and it is not a volume-related quantity.
What input does it reject?
Zero and negative values return “Value must be positive”, whichever measurement you chose. Blank fields are not valid. Everything else positive is accepted, including decimals such as 0.5.
What units are the results in?
Radius, diameter and circumference share your length unit. Surface area is that unit squared and volume is that unit cubed. If you pick surface area as the known value, enter it in square units already, for example cm², or the derived radius will be wrong.
What happens when I double the radius?
Surface area multiplies by 4 and volume by 8. A sphere of radius 1 has an area of 12.566371 and a volume of 4.18879. At radius 2 you would get four times the area and eight times the volume. This explains why larger bodies have less surface per unit volume.
Does it do hemispheres or spherical caps?
No. It handles only the complete sphere. For a hemisphere you would halve the volume and, for a solid one, add the flat circular face to half the surface area; those steps are not performed here.
Sphere radius, area and volume from any one measurement
One measurement is enough
A sphere is fixed completely by its radius, so any single measurement determines all the others. Choose which one you know, enter it, and the calculator works out the radius first, then the diameter (2r), surface area (4πr²), volume (4/3πr³) and great-circle circumference (2πr). Surface area and volume are linked by V = A × r ÷ 3, so a sphere with radius 6 has a volume equal to its area times 2.
| Known value | Radius | Surface area | Volume |
|---|---|---|---|
| Radius 6 | 6 | 452.389342 | 904.778684 |
| Diameter 26 | 13 | 2123.716634 | 9202.77208 |
| Surface area 100 | 2.820948 | 100 | 94.031597 |
| Volume 1000 | 6.203505 | 483.597586 | 1000 |
| Radius 1 | 1 | 12.566371 | 4.18879 |
Worked example: starting from the diameter
A ball measures 26 across. Selecting Diameter and entering 26 gives a radius of 13, a surface area of 2123.716634 and a volume of 9202.77208. The great-circle circumference is 81.681409, which is the length of a tape measure wrapped around its widest part. Because only the diameter was measured, no other length is assumed.
Worked example: working backwards from a volume
Suppose a spherical tank holds 1000 cubic units. Choosing Volume and entering 1000 gives a radius of 6.203505, a diameter of 12.40701 and a surface area of 483.597586. The surface area figure tells you how much material is needed to cover the outside. Notice that a volume of 1000 needs less than 500 units of surface, since the sphere is the shape with the smallest surface for a given volume.
Scaling with size
Lengths scale with the radius, areas with its square, volumes with its cube. Radius 0.5 gives a surface area of 3.141593, which equals π, and a volume of 0.523599. Moving to radius 1 gives 12.566371 and 4.18879: four times the area, eight times the volume. When comparing two spheres, work with the ratio of radii and square or cube it, instead of recomputing from scratch.
Rounding and consistency
Every figure is rounded to six decimal places for display, though the calculation itself keeps full precision. When you enter a surface area or volume, the same quantity comes back unchanged, which is a quick way to confirm the unit you assumed. A sphere is the only shape handled here; hemispheres and caps need separate formulas.
Learn more from an authoritative source:
WikipediaCylinder Calculator
Calculate the volume, lateral surface area, total surface area, and base area of a cylinder from its radius and height.
Percentage Difference Calculator
Calculate the symmetric percentage difference between two values — useful when neither value is a reference baseline.
Percent Error Calculator
Calculate the percent error between an experimental measurement and the accepted theoretical value, including absolute error and sign.
Absolute Value Calculator
Calculate the absolute value of any real number, with a step-by-step explanation of the result.
Cube Root Calculator
Calculate the cube root of any real number. Shows exact result for perfect cubes, decimal approximation for others, and the verification check.
Reciprocal Calculator
Calculate the reciprocal of a number or fraction. Enter a whole number or numerator/denominator — get the reciprocal as a fraction and decimal.
Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →