Radius of a Sphere Calculator
Calculate the radius of a sphere using diameter, surface area, volume, or other geometric parameters
Calculate Sphere Radius
The distance across the sphere through its center
Calculation Results
Formula used: r = d / 2
Calculation Analysis
Example Calculation
Earth's Radius Example
Problem: Earth has approximately a volume of 1.083 × 10¹² km³
Given: Volume = 1,083,206,916,846 km³
Find: Earth's radius (approximating Earth as a perfect sphere)
Solution
Using formula: r = ∛(3V / (4π))
r = ∛(3 × 1,083,206,916,846 / (4π))
r = ∛(3,249,620,750,538 / 12.566)
r = ∛(258,618,739,478)
r ≈ 6,371 km
Note: Earth's actual radius ranges from 6,357-6,378 km due to its oblate shape.
Sphere Formulas
Basic Properties
d = 2r
C = 2πr
Surface Area
A = 4πr²
Volume
V = (4/3)πr³
SA:V Ratio
A/V = 3/r
Radius Formulas
From Diameter
r = d / 2
From Surface Area
r = √(A / (4π))
From Volume
r = ∛(3V / (4π))
From SA:V Ratio
r = 3 / (A/V)
Calculator Tips
Choose the method based on known parameters
Ensure all input values use consistent units
Radius is half the diameter
Spheres have the lowest SA:V ratio for given volume
Great circle circumference equals 2πr
Understanding Sphere Radius Calculations
What is a Sphere Radius?
The radius of a sphere is the distance from the center of the sphere to any point on its surface. A sphere is a perfectly round 3D object where all points on the surface are equidistant from the center. It's the 3D analog of a circle in 2D space.
Key Properties
- •All radii of a sphere are equal in length
- •Diameter equals twice the radius
- •Volume grows with the cube of radius
- •Surface area grows with the square of radius
Common Applications
- •Astronomy and planetary science
- •Engineering and manufacturing
- •Physics and chemistry (atomic models)
- •Sports ball specifications
- •Volume and capacity calculations
Fun Fact: Among all 3D shapes with the same volume, a sphere has the smallest surface area. This is why soap bubbles naturally form spheres!
Formula Derivations
From Surface Area
A = 4πr²
r² = A / (4π)
r = √(A / (4π))
From Volume
V = (4/3)πr³
r³ = 3V / (4π)
r = ∛(3V / (4π))
Practical Measurement Tips
Water Displacement Method
- 1. Fill a container with water
- 2. Submerge the sphere completely
- 3. Measure the displaced water volume
- 4. Use V = (4/3)πr³ to find radius
Direct Measurement
- 1. Use calipers to measure diameter
- 2. Ensure measurement passes through center
- 3. Divide diameter by 2 to get radius
- 4. Take multiple measurements for accuracy