Sphere Surface Area Calculator
Surface area of a sphere from radius, in metric and imperial.
What it does
A sphere wraps the most volume in the least skin of any solid, and its skin follows 4πr². Radius 5 gives 100π at 314.16 square units, while diameter form says the same through πd².
The tool above takes radius in centimeters or inches. It returns surface area with diameter and enclosed volume beside it. The default radius 5 gives 314.16 cm2 with diameter 10 cm and volume 523.6 cm3.
Geometry sources state the pair together: volume at four thirds πr³ with surface at 4πr², worked at radius 6 inches and on a 14 inch globe. Surface is the derivative of volume in r, which is why the 4 and the 4/3 arrive together.
Schoolbook 3.14 rounds the same answers a hair low: radius 6 reads 452.16 against the exact 452.39. Either suffices for paint and crafts; keep full pi for machining.
How to use
- Pick centimeters or inches.
- Type the radius, half the diameter.
- Read surface first, diameter beside it.
- Check: pi times diameter squared must match.
- Use volume only as a bonus cross check.
- Convert mirrors land together through 6.4516.
Formula
- r
- Sphere radius, half the diameter.
- d
- Full diameter, twice the radius.
- V
- Enclosed volume shown for contrast.
Imperial inputs convert to centimeters first (x 2.54), then divide square centimeters by 6.4516 for square inches. Volume lives on its own page; here it only checks scale.
Worked example
Example: radius 5
Metric default: radius 5 cm.
- Square: 5 x 5 = 25.
- Surface: 4 x 3.14159 x 25 = 314.16 cm2.
- Diameter: 2 x 5 = 10 cm; pi x 100 matches.
- Volume: 4/3 x pi x 125 = 523.6 cm3.
- Imperial check: 1.97 in gives 48.77 in2.
- Tool shows 314.16 cm2, 10 cm, 523.6 cm3.
Reference table
| Radius | Surface | Volume |
|---|---|---|
| 1 cm | 12.57 cm2 | 4.2 cm3 |
| 5 cm | 314.16 cm2 | 523.6 cm3 |
| 6 in | 452.39 in2 | 904.8 in3 |
| 14 in globe | 2463.01 in2 | 11494 in3 |
Limits
- Perfect spheres; spheroids differ.
- Radius input; diameters must halve.
- Paint needs coats and waste factors.
- Hollow shells need thickness math.
Common mistakes
- Feeding diameter as radius, quadrupling area.
- Using volume formula for surface.
- Mixing cm and inches in one calculation.
- Reporting cubic units for an area.
- Trusting 3.14 for precision work.
Try it yourself
Quick checks. Answers sit tucked under each question.
Radius 6 in?
452.39 in2 with diameter 12 in.
Radius 1 cm?
12.57 cm2.
Diameter 10?
Radius 5, so 314.16 area units.
Questions
What is the sphere formula?
4 times pi times r squared; pi d squared from diameter.
Default answer?
314.16 cm2 at radius 5.
Volume page versus this?
That solves 4/3 πr³; this solves 4πr² with volume as a bonus.
OpenStax 452.16?
Schoolbook pi 3.14; exact is 452.39.
Do units convert?
Yes: 314.16 cm2 is 48.77 in2.
Hemisphere?
Half the surface plus the base circle: 2πr² + πr².