🔮 Sphere Surface Area Calculator
Calculate Surface Area Using 4πr² Formula
Perfect for balls, globes, domes & spherical objects
Sphere Surface Area Calculator
⭕ Enter Radius
🔮 Sphere vs 🌓 Hemisphere
📊 Calculation Steps
Sphere Formulas
Surface Area
Where r = radius
Surface Area (from Diameter)
Volume
Radius from Surface Area
Radius from Volume
Hemisphere Formulas
| Property | Formula | Description |
|---|---|---|
| Curved Surface Area | 2πr² | Dome part only |
| Base Area | πr² | Flat circular base |
| Total Surface Area | 3πr² | Curved + base |
| Volume | (2/3)πr³ | Half of sphere volume |
Example Calculations
| Radius | Diameter | Surface Area (4πr²) | Volume (4/3)πr³ | Circumference |
|---|---|---|---|---|
| 1 | 2 | 12.57 | 4.19 | 6.28 |
| 2 | 4 | 50.27 | 33.51 | 12.57 |
| 3 | 6 | 113.10 | 113.10 | 18.85 |
| 5 | 10 | 314.16 | 523.60 | 31.42 |
| 10 | 20 | 1256.64 | 4188.79 | 62.83 |
Real-World Spheres
| Object | Approximate Radius | Surface Area |
|---|---|---|
| Basketball | 12 cm | 1,809.6 cm² |
| Soccer Ball | 11 cm | 1,520.5 cm² |
| Golf Ball | 2.1 cm | 55.4 cm² |
| Earth | 6,371 km | 510.1 million km² |
| Moon | 1,737 km | 37.9 million km² |
How to Calculate Sphere Surface Area
- Measure the radius — Find the distance from the center to any point on the surface.
- Square the radius — Calculate r² (radius × radius).
- Multiply by 4π — Use 4 × 3.14159 × r² to get the surface area.
- Include units — Remember to use square units (cm², m², etc.).
- For hemisphere — Use 3πr² for total area (curved + base).
Educational Resources
Frequently Asked Questions
The surface area of a sphere is SA = 4πr², where r is the radius. Using diameter (d = 2r), the formula becomes SA = πd². This equals 4 times the area of a circle with the same radius.
Archimedes proved that a sphere's surface area equals 4 circles of the same radius. This can be visualized by projecting the sphere onto a cylinder — the curved surface of the cylinder (2πr × 2r = 4πr²) exactly equals the sphere's surface.
A sphere is a complete ball. A hemisphere is half a sphere (like a dome). Hemisphere surface area includes curved part (2πr²) plus flat base (πr²) = 3πr² total.
Rearrange the formula: r = √(SA/4π). For example, if SA = 314.16 cm², then r = √(314.16/12.566) = √25 = 5 cm.
Use SA = πd² where d is the diameter. Or first convert to radius (r = d/2) and use SA = 4πr². Both give the same answer.
The curved surface area (dome part only) is 2πr². This is half of the full sphere's surface area. Add πr² for the base to get total hemisphere surface area = 3πr².
Surface area = 4πr² measures the outer skin. Volume = (4/3)πr³ measures interior space. The ratio SA/V = 3/r, meaning smaller spheres have relatively more surface area compared to volume.
For estimates, use π ≈ 3.14 or 22/7. For precision, use the full value π = 3.14159265... This calculator uses the full mathematical constant for accuracy.
Spheres appear in: sports (balls), astronomy (planets, stars), engineering (tanks, domes), medicine (cells, pills), packaging (spherical containers), and architecture (geodesic domes).
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Last Updated: January 2026