Surface Area Calculator
Find the total, curved (lateral) and base surface area of a cube, cuboid, sphere, cylinder, cone, hemisphere or triangular prism, with formulas and steps.
Result
Cylinder · r = 3 cm, h = 10 cm
Curved surface area
188.5 cm²
= 60π cm²
Area of both circular bases
56.55 cm²
= 18π cm²
Surface area of a cylinder
SA = 2πr(r + h)
SA = 2 × π × 3 × (3 + 10)
SA = 78π cm² ≈ 245.04 cm²
| Surface | Formula | Area (cm²) |
|---|---|---|
| Curved surface area | 2πrh | 60π =≈ 188.5 |
| One circular base | πr² | 9π =≈ 28.27 |
| Both circular bases | 2πr² | 18π =≈ 56.55 |
| Total surface area | 2πr(r + h) | 78π =≈ 245.04 |
For an open tube with no ends, use the curved surface area only; for a cup with one end, add one base.
Step-by-step calculation
Step 1: Given
Radius: r = 3 cm
Height: h = 10 cm
Step 2: Formula
Two circular bases (2πr²) plus the curved side, which unrolls into a rectangle 2πr wide and h tall (2πrh).
SA = 2πr² + 2πrh = 2πr(r + h)
Step 3: Substitute
SA = 2 × π × 3 × (3 + 10)
Step 4: Calculate
Curved surface = 2πrh = 2 × π × 3 × 10 = 60π ≈ 188.5
Both bases = 2πr² = 2 × π × (3)² = 18π ≈ 56.55
SA = 2 × π × 3 × 13 = 78π ≈ 245.04
Step 5: Result
SA = 78π cm² ≈ 245.04 cm²
Surface area formulas
r = radius, h = height, l = slant height (cone), a, b, c = triangle sides, L = prism length, s = (a + b + c)/2, T = triangle area.
| Shape | Total surface area | Lateral / curved | Base |
|---|---|---|---|
| Cube | 6a² | 4a² | a² (each face) |
| Cuboid / rectangular prism | 2(lw + lh + wh) | 2h(l + w) | lw |
| Sphere | 4πr² | 4πr² (all curved) | none |
| Cylinder | 2πr(r + h) | 2πrh | πr² (each end) |
| Cone | πr(r + l), with l = √(r² + h²) | πrl | πr² |
| Hemisphere (solid) | 3πr² | 2πr² | πr² |
| Triangular prism | 2T + (a + b + c)L | (a + b + c)L | T = √(s(s − a)(s − b)(s − c)) |
Lateral area leaves out the bases: for a cube or cuboid it is the four side faces (top and bottom are the bases); for a prism, the rectangles. The hemisphere total includes its flat face; the cone is a right circular cone; the prism is a right prism.
π is used at full precision and nothing is rounded until the final display. To find how much a shape holds, use the Volume Calculator; for circles and triangles on their own, see the Circle Calculator and Triangle Calculator. Convert an answer with the Area Converter (1 m² = 10,000 cm²), or turn a wall area into paint with the Paint Calculator.
Surface area is the total area of all the outside surfaces of a 3D object: the amount of paint, wrapping or sheet material it takes to cover it completely. This surface area calculator finds the total surface area of a cube, cuboid (rectangular prism), sphere, cylinder, cone, hemisphere or triangular prism, and splits it into the curved or lateral surface and the base areas.
Choose a shape, enter its dimensions in millimeters, centimeters, meters, kilometers, inches, feet or yards, and the answer appears in the matching square unit, such as cm² or ft². Each result shows the formula, the numbers substituted into it, an exact value in terms of π where one exists (for example 100π cm²), and the full step-by-step working next to a labelled diagram of the shape.
Worked Calculation Examples
| Scenario | Result | Calculation Step |
|---|---|---|
| Cube with side 4 cm | 96 cm² | SA = 6a² = 6 × 4² = 6 × 16 = 96 cm². Each face is 16 cm², and the four side faces alone (lateral area) make 4 × 16 = 64 cm². |
| Cylinder: radius 3 cm, height 10 cm | 78π ≈ 245.04 cm² | Curved surface = 2πrh = 2π × 3 × 10 = 60π ≈ 188.50 cm². Both bases = 2πr² = 2π × 9 = 18π ≈ 56.55 cm². Total = 2πr(r + h) = 2π × 3 × 13 = 78π ≈ 245.04 cm². |
| Sphere with radius 5 m | 100π ≈ 314.16 m² | SA = 4πr² = 4 × π × 5² = 4 × π × 25 = 100π ≈ 314.16 m². The whole surface is curved, so this is also the curved surface area. |
| Cone: radius 3 in, height 4 in | 24π ≈ 75.40 in² | First the slant height: l = √(3² + 4²) = √25 = 5 in. Curved surface = πrl = π × 3 × 5 = 15π ≈ 47.12 in². Base = πr² = 9π ≈ 28.27 in². Total = πr(r + l) = π × 3 × 8 = 24π ≈ 75.40 in². |
| Rectangular prism 8 ft × 5 ft × 3 ft | 158 ft² | SA = 2(lw + lh + wh) = 2(40 + 24 + 15) = 2 × 79 = 158 ft². Without the top and bottom, the lateral area is 2h(l + w) = 2 × 3 × 13 = 78 ft². |
| Hemisphere with radius 7 cm | 147π ≈ 461.81 cm² | Curved surface = 2πr² = 2π × 49 = 98π ≈ 307.88 cm². Flat base = πr² = 49π ≈ 153.94 cm². Total = 3πr² = 147π ≈ 461.81 cm². An open bowl of this size has only the 98π cm² curved surface. |
| Triangular prism: sides 3, 4, 5 m, length 10 m | 132 m² | The 3-4-5 end is a right triangle, so its area is ½ × 3 × 4 = 6 m² (Heron’s formula gives the same). Both ends = 12 m². The three rectangles = (3 + 4 + 5) × 10 = 120 m². Total = 12 + 120 = 132 m². |
What Is Surface Area?
The surface area of a solid is the combined area of every surface on its outside. Imagine peeling the surface off and laying it flat: a cube opens into six squares, a cylinder into two circles and a rectangle, and a cone into a circle and a sector. Adding those flat pieces gives the surface area.
Because it is an area, surface area is measured in square units. A cube with 4 cm edges has six faces of 4 × 4 = 16 cm² each, so its surface area is 6 × 16 = 96 cm².
Total, Lateral, Curved and Base Surface Area
Total surface area (TSA) includes every face: the sides and the ends. Base area is the area of the end faces a solid stands on: the two circles of a cylinder, the circle under a cone, the two triangles of a triangular prism, or the top and bottom of a box.
Lateral surface area is everything except the bases, meaning the side faces of a prism or box. For solids with a curved side it is called the curved surface area (CSA): 2πrh for a cylinder, πrl for a cone and 2πr² for a hemisphere. So for a cylinder, TSA = CSA + 2 × base area = 2πrh + 2πr². A sphere has no bases, so its total and curved surface areas are the same, 4πr².
Which one you need depends on the object. A closed can needs the total surface area, a label wrapped around the can needs only the curved surface area, and an open tank needs the curved surface plus one base.
Surface Area vs Volume
Surface area measures the outside of a solid, the amount of exposed area, in square units such as cm², m² or ft². Volume measures the three-dimensional space inside it, in cubic units such as cm³, m³ or ft³. Surface area tells you how much paint or wrapping you need; volume tells you how much the shape holds.
The two grow at different rates. A cube with 2 cm edges has a surface area of 24 cm² and a volume of 8 cm³. Double the edges to 4 cm and the surface area becomes 96 cm² (4 times as much) while the volume becomes 64 cm³ (8 times as much). Scaling every length by k multiplies surface area by k² and volume by k³, which is why small objects have much more surface per unit of volume than large ones.
Units: Why Surface Area Uses Square Units
Every piece of surface is a length times a length, so surface area always comes out in square units. If you enter dimensions in centimeters, the result is in cm²; in feet, it is in ft². Always convert all dimensions to the same unit before you start: mixing 50 cm with 2 m gives a wrong answer.
Converting areas uses the square of the length factor. Since 1 m = 100 cm, 1 m² = 100 × 100 = 10,000 cm², not 100 cm². Likewise 1 ft² = 144 in² and 1 yd² = 9 ft².
Real-World Uses of Surface Area
Painting and coating: the surface area of walls, a tank or a pipe, divided by the coverage on the paint can, gives the amount of paint, varnish or galvanizing needed. Packaging and manufacturing: the surface area of a box or can is roughly the amount of cardboard, sheet metal or plastic needed to make it, so designers compare shapes that hold the same volume to use less material.
Construction and material estimates: roofing, cladding, insulation and plaster are ordered by area, and cylindrical tanks or domes use the curved-surface formulas. Heat transfer and engineering: heat flows through a surface in proportion to its area, which is why radiators and heat sinks have fins and why a sphere, the shape with the least surface for its volume, loses heat most slowly. Container design: a cylindrical can holds the most for the least metal when its height equals its diameter.
How to Use the Surface Area Calculator
- Choose the shape: cube, cuboid (rectangular prism), sphere, cylinder, cone, hemisphere or triangular prism. The diagram updates to show which dimensions to measure.
- Enter the dimensions shown. For a cone, choose whether you know the perpendicular height or the slant height; for a triangular prism, enter the three sides of the triangular end and the prism length.
- Pick the unit your measurements are in (mm, cm, m, km, in, ft or yd). All dimensions must use the same unit, and the answer is given in that unit squared.
- Read the total surface area, the curved or lateral area and the base area. Where the answer is a whole multiple of π, the exact form (such as 100π cm²) is shown next to the decimal.
- Follow the step-by-step working to see the formula, the substituted values and each calculation, and choose how many decimal places to display.
Frequently Asked Questions
What is surface area?
Surface area is the total area of all the outside surfaces of a 3D object, the area you would cover if you wrapped or painted it completely. It is measured in square units such as cm², m² or ft².
How do you calculate surface area?
Find the area of every face or curved surface of the solid and add them together, or use the shape’s formula, which does that in one step. For a box, add the areas of its six rectangles; for a cylinder, add two circles (2πr²) and the curved side (2πrh).
What is the difference between surface area and volume?
Surface area measures the outside of a shape in square units, such as how much paint covers it. Volume measures the space inside in cubic units, such as how much water it holds. A 2 cm cube has a surface area of 24 cm² and a volume of 8 cm³.
What is the surface area formula for a cube?
SA = 6a², where a is the side length. A cube has six identical square faces, each of area a². For a = 4 cm, SA = 6 × 16 = 96 cm².
How do you calculate the surface area of a cylinder?
Use SA = 2πr(r + h), which is the two circular ends (2πr²) plus the curved side (2πrh). For r = 3 cm and h = 10 cm, SA = 2π × 3 × 13 = 78π ≈ 245.04 cm².
How do you calculate the surface area of a sphere?
Use SA = 4πr², where r is the radius. For r = 5 m, SA = 4 × π × 25 = 100π ≈ 314.16 m². If you know the diameter, halve it first.
What is the difference between total and lateral surface area?
Total surface area includes every face, bases included. Lateral surface area leaves the bases out: for a cylinder it is only the curved side, 2πrh, and for a box it is the four side faces, 2h(l + w).
What units are used for surface area?
Square units matching the length unit: mm², cm², m², km², in², ft² or yd². Enter all dimensions in the same unit. To convert, square the length factor: 1 m² = 10,000 cm² and 1 ft² = 144 in².
Why is surface area measured in square units?
Every piece of a surface is two-dimensional, so its area is a length multiplied by a length. Centimeters times centimeters gives square centimeters (cm²), even when the surface is curved.
How do you find the surface area of a cone?
Use SA = πr(r + l), where l is the slant height: the base πr² plus the curved surface πrl. If you know the height h instead, find l = √(r² + h²) first. For r = 3 and h = 4, l = 5 and SA = 24π ≈ 75.40 square units.
Related Calculators
Geometry Volume Calculator
Find the volume of a cube, cuboid, sphere, cylinder, cone, hemisphere, triangular prism or pyramid, with exact and decimal answers and steps.
Circle Calculator
Find radius, diameter, circumference, and area from any one of them, plus arc length, sector area, chords, central angles, and segments.
Triangle Calculator
Solve any triangle from what you know: three sides, two sides and an angle, two angles and a side, a right triangle, or base and height.
Area Converter
Convert square feet, square meters, acres, and hectares.
Paint Calculator
Calculate paint gallons required for wall square footage.
Length Converter
Convert meters, feet, inches, miles, and kilometers.
Last updated: September 27, 2026.