Sphere Calculator
Calculate the volume and surface area of a sphere from its radius
Enter the radius. Volume is (4/3)πr³ and surface area is 4πr². The units are whatever units you used for the radius: a radius in inches gives cubic inches and square inches.
Calculator Inputs
Results
Enter values above to see your results
How to use this calculator
- Measure the radius, which is half the diameter.
- Enter that number. Do not enter the diameter unless you divide it by 2 first.
- Read the volume and the surface area.
How the calculation works
Volume is four thirds times π times the radius cubed. Surface area is 4 times π times the radius squared.
A radius of 3 makes both formulas equal 36π, about 113.1. That is a property of radius 3, not a display error. At any other radius the two numbers separate.
Radius of 3
(4/3)π × 3³ = (4/3)π × 27 = 36π. Surface area is 4π × 3² = 36π. Both are 113.1 when rounded to one decimal place.
Worked example
Radius 3
(4/3) × π × 3³= 113.14 × π × 3²= 113.1Tips & Best Practices
- •If you measured a diameter, divide by 2 before you enter it.
- •Keep the same unit for the radius that you want on the volume and area.
Frequently Asked Questions
How do you find the volume of a sphere?
Use (4/3)πr³. For a radius of 3, that is 36π, or 113.1.
How do you find the surface area of a sphere?
Use 4πr². For a radius of 3, that is also 36π, or 113.1.
Why are volume and surface area the same at radius 3?
Because (4/3)πr³ and 4πr² both equal 36π when r is 3. Change the radius and the numbers differ.