Sphere Surface Area Calculator
The surface area of a sphere is A = 4 π r², and this sphere surface area calculator works it out the instant you enter a radius (or diameter). A sphere has no flat faces, so its curved surface area and total surface area are the same. You'll also get the curved and total surface area of a hemisphere, solid or hollow, plus the answer in terms of pi and the formula and steps with every result.
- Curved & total area
- Sphere or hemisphere
- Solid or hollow
- Radius or diameter
- In terms of pi
Last updated June 15, 2026 Method: A = 4πr² Reviewed by the Calcowa math team
Enter a positive radius to see the surface area.
Show all units
A = 4π × 5² = 314.16 in²
What is the surface area of a sphere?
The surface area of a sphere is the area of its whole outer skin, found with A = 4 × π × r². For a radius of 5 in, the sphere surface area is about 314.2 square inches.
Because a sphere is curved everywhere and has no flat faces, its curved surface area (CSA) and its total surface area (TSA) are the same value, 4πr². That's why a search for the curved surface area of a sphere and the total surface area of a sphere both lead to one formula. Same answer, two names.
How do you calculate the surface area of a sphere?
To find the surface area of a sphere, square the radius, then multiply by 4 and by pi. Here's the full sequence:
- 1
Measure the radiusMeasure the radius. If you only have the diameter, divide it by 2.
- 2
Square the radiusMultiply the radius by itself to get r squared.
- 3
Multiply by 4 and piMultiply r squared by 4 and by pi (about 3.14159).
- 4
Read the areaThat's the surface area of the sphere in square units.
- 5
Convert the unitsConvert to square feet or square meters if that's what you need.
Curved and total surface area of a hemisphere
A hemisphere is half a sphere, so it has a curved part and a flat circular base. The curved surface area of a hemisphere is 2πr², exactly half the sphere's curved area. The total surface area adds the flat base circle, πr², so TSA = 2πr² + πr² = 3πr². Switch the calculator to Hemisphere and it shows the curved (CSA) and total (TSA) values side by side, which is the pair most class questions ask for.
Total surface area of a hollow hemisphere
A hollow hemisphere, like a bowl with a wall, has an outer surface, an inner surface, and a flat ring around the rim. Its total surface area is π(3R² + r²), where R is the outer radius and r is the inner radius. That breaks down into the outer curved part 2πR², the inner curved part 2πr², and the rim ring π(R² - r²).
Set the shape to Hemisphere and the wall to Hollow, then enter both radii. The calculator adds the inner and outer skins and the rim for you, which is what you need for bowls, shells, and dome covers.
Curved surface area vs total surface area
Curved surface area (CSA) counts only the rounded part of a shape, while total surface area (TSA) counts every face. For a full sphere they're equal, both 4πr², since the whole sphere is curved. For a hemisphere they differ: the CSA is 2πr² and the TSA is 3πr², because the TSA also includes the flat base. The result panel labels both, so you'll never mix them up.
Surface area of a sphere from the diameter
If you measured the diameter across the widest point, halve it to get the radius (r = d ÷ 2) and then use A = 4πr². You can also work straight from the diameter with A = πd², which gives the same answer. Switch the calculator to Diameter and it'll halve the value for you, so the surface area of a sphere from the diameter takes one entry.
A surface area example, step by step
Say you've got a sphere with a radius of 7 cm. Square the radius to get 49, then multiply by 4 and by pi.
A = 4π × 7² = 196π ≈ 615.75 cm²
curved area = total area, since a sphere has no flat faces
Type a radius of 7 and pick centimeters above, and you'll get the matching square meters and square inches at once.
Units and accuracy
Calcowa shows the sphere surface area in square millimeters, centimeters, meters, inches, feet, and yards at once, plus the exact answer in terms of pi. The results use the full value of pi, not a rounded 3.14, so they're accurate for engineering, school, and material estimates.
| Unit | Best for | Good to know |
|---|---|---|
| Square inches (in²) | Balls, bearings, small domes | Default when you enter inches |
| Square feet (ft²) | Tanks, domes, painting jobs | 1 ft² = 144 in² |
| Square centimeters (cm²) | Lab and school work | 1 in² = 6.4516 cm² |
| Square meters (m²) | Large spheres and tanks | 1 m² = 10.7639 ft² |
| In terms of pi (π) | Exact math answers | Leaves the result as a multiple of pi |
Frequently asked questions
Is the curved surface area of a sphere the same as the total surface area?
Yes. A sphere has no flat faces, so its curved surface area and total surface area are both 4πr². They only differ for shapes with flat parts, like a hemisphere, where the total adds the base circle to the curved 2πr².
A sphere's curved surface area is the same as its total surface area, A = 4 × π × r², because a sphere has no flat faces. So for a sphere, CSA and TSA both equal 4πr². For a radius of 5 in, that's about 314.2 square inches.
The curved surface area of a hemisphere is 2πr², which is half the sphere's curved area. The total surface area adds the flat circular base, so TSA = 2πr² + πr² = 3πr². Use the Hemisphere setting to switch between the curved and total values.
A hollow hemisphere, like a bowl with a wall, has a total surface area of π(3R² + r²). That's the outer curved part (2πR²) plus the inner curved part (2πr²) plus the ring at the rim, π(R² - r²). Switch on the hollow option and enter both radii.
Divide the diameter by 2 to get the radius, then use A = 4πr². You don't have to do that by hand: set the measurement to Diameter and the calculator halves it for you first.
Archimedes showed that a sphere has exactly the same surface area as the curved side of the cylinder that just wraps around it, which is 2πr × 2r = 4πr². Calculus gives the same result by adding up thin rings over the surface.
A sphere doesn't have a perimeter, but the distance around its widest circle, the great circle, is C = 2πr (or πd). People often mean that great-circle circumference when they ask for the perimeter of a sphere.
The outer skin of a sphere is called the spherical surface, and its area is 4πr². There are no edges or flat faces, so the whole surface is curved, which is why the curved area and the total area are the same number.
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Need a sphere surface area fast?
Try the calculator above, or browse every shape in the geometry hub.