Sphere surface area calculator

Calculate a sphere’s surface area from its radius using 4πr². Includes a worked example and square-unit results.

Result

Four equivalent discs

A sphere’s surface area equals four discs with the same radius. This compares areas; it is not a distortion-free flat net.

How do you calculate sphere surface area?

Multiply the radius squared by π and four. The result measures the outer covering in square units, not cubic units.

S = 4 \times π \times r^{2}

r = \frac{d}{2}

How to use the calculator

Enter measurements with a decimal point or comma: results update immediately. Input units apply to every length; changing them converts the measurements. Changing result units leaves the shape unchanged. The control below the drawing reveals or hides its visual explanation. Copy results includes valid measurements and the result. Reset and Try this example restore the initial values and centimetre units.

Choose radius or diameter: switching preserves the shape’s dimensions. Drawing handles always change the radius and also update the diameter when selected.

The first formula shows the relationship; the second substitutes measurements converted to the result unit. The ≈ sign indicates rounding, including in the substituted values.

Covering a sphere

A sphere with radius 3 cm has surface area 36π cm², approximately 113.10 cm². A disc with that radius covers 9π cm², so four discs have the same total area.

From measurements to the result

Input: $r = 3 cm$
Result: $≈ 113.1 {cm}^{2}$

Calculation steps

Square the radius.
$r^{2} = 3^{2} = 9$
Complete the calculation using the tool’s formula.
$S = 4 \times 9 \times π = 36 \times π$

Units and interpretation

Area uses square units: 1 m² = 10,000 cm².

The ideal covering does not include waste, overlaps or the distortion needed to fit flat material around a sphere.

Precision and numerical limits

Lengths range from 0 to 10¹² in the selected unit; triangle sides must be strictly positive. Results use two decimal places, with scientific notation for very small or large values. Calculations use browser precision: unrepresentable positive values produce an error. A rejected unit change keeps the previous data. Calculation takes place in your browser.

Maximum diameter is 10¹² in the input unit. A rejected mode change keeps the previous data.

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Sphere surface area calculator

Result

Four equivalent discs

How do you calculate sphere surface area?

How to use the calculator

Covering a sphere

From measurements to the result

Calculation steps

Units and interpretation

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