Surface area calculator
This surface area calculator covers eight solids: pick the shape, enter the measures, done. A cylinder with r = 3 cm and h = 10 cm has a surface area of 245.04 cm² and a volume of 282.74 cm³, shown with the steps and the capacity in litres.
Example: Solid: Cylinder · Radius r 3 · Height h 10 · Unit: Centimetres → Result: Surface area A = 245.0442 cm² · Volume V = 282.7433 cm³. Source: Wikipedia – Surface area. Updated: .
How it is calculated
The surface area is the sum of all faces that bound a solid. It is measured in square units (cm², m²) and is what you need for paint, wrapping, insulation or sheet metal. The volume is measured in cubic units and tells you how much fits inside.
The formulas at a glance
- Cube: A = 6 · a²
- Cuboid: A = 2 · (ab + ac + bc)
- Cylinder: A = 2πr · (r + h)
- Cone: A = πr · (r + s) with s = √(r² + h²)
- Sphere: A = 4πr²
- Hemisphere: A = 3πr² (curved surface plus the flat circle)
- Square pyramid: A = a² + 2as with s = √(h² + (a/2)²)
- Torus: A = 4π²Rr
How to use the calculator
Choose the solid, enter the measures in one common unit and select that unit. You get the surface area, lateral area, base area, volume and the capacity in litres. Example: a cuboid of 4 × 3 × 2 cm has A = 2 · (12 + 8 + 6) = 52 cm² and V = 24 cm³.
Frequently asked questions
How do you calculate the surface area of a cylinder?
A = 2πr² + 2πrh: two circles plus the curved side. For r = 3 and h = 10 that is 56.55 + 188.50 = 245.04 (in square units).
What is the difference between surface area and lateral area?
Lateral area is only the side surface without the base and top. Total surface area includes every face, so for a cylinder both circles as well.
How do you find the surface area of a sphere?
A = 4πr². With r = 5 that is 314.16. A hemisphere has A = 3πr² because the flat cut face is added.
What unit is surface area measured in?
In the square of the length unit: measures in cm give cm², in m give m². The calculator also shows the area in m².
How do I convert volume to litres?
1 dm³ equals 1 litre, so 1,000 cm³ = 1 litre and 1 m³ = 1,000 litres. The calculator gives the capacity in litres directly.
Sources and legal basis
As of: · Editorial policy
Related tools
- Volume CalculatorVolume calculator for 12 shapes: cylinder, box, sphere, cone, prism, horizontal tank … Mix cm, m, inches and feet – with litres, gallons, formula and sketch.
- Cone calculatorCone calculator: from radius and height, radius and slant height, or height and slant height get volume, lateral area, surface area and angle with formulas.
- Sphere calculatorSphere calculator: enter the radius, diameter, volume, surface area or circumference and get every measure of the sphere with formulas and steps. Free.
- Cylinder CalculatorCylinder calculator from any two values: radius, diameter, circumference, height, volume, lateral or surface area – with formulas, litres and working.
- Rectangular prism calculatorRectangular prism calculator: from length, width and height (or volume) get surface area, lateral area, space diagonal and edge sum, with formulas and steps.
- Online CalculatorCalculator online, free and instant: type or tap and see the answer as you go – order of operations, brackets, percent, square root, steps and a history list.
- Stem and Leaf Plot GeneratorStem and leaf plot generator: enter your numbers and get stems and leaves sorted automatically, with a key, split stems and the median.
- Hex to decimal and decimal to hex converterHex to decimal: multiply each digit by a power of 16, so FF = 255. Type hex for decimal, binary and octal, or go back from decimal, with the working.
- Binary to decimal and decimal to binary converterBinary to decimal: add the powers of 2 where there is a 1, so 1011 = 11. Type bits for decimal, hex and octal, or go back from decimal, with the working.