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Surface Area Calculator

Find the total, side (lateral) and base surface area of a cube, box, cylinder, sphere, cone or rectangular pyramid, in your choice of units.

Level: Grades 6–8

  • Common Core standard 6.G.A.4Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
  • Common Core standard 7.G.B.6Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
Printable worksheet

Surface Area Calculator

Know the answer you need? Pick an input to work backward.

Inputs

Result

Total surface area

52 ft²

The total surface area is 52 ft².

Lateral area (sides only)
28 ft²
Base area
12 ft²
In square meters
4.831 m²

See the step-by-step solution ↓

Step-by-step solution

  1. A box has three pairs of matching rectangles, so add one of each and double it

    2×(4×3+4×2+3×2)=2×(12+8+6)=52 ft²

  2. To convert to square meters, multiply by (1 ft in meters)²

    52 ft²×0.30482=4.830958 m²

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Find how much outside surface a box, can, ball, cone or pyramid has, for wrapping, painting or labeling. Surface area is the total area of every face of a solid. Think of the wrapping paper that covers a box, the sheet metal in a can, or the paint on a ball. It's measured in square units. Volume, the space inside, is measured in cubic units.

Pick a shape and the unit you measured in, then enter its sizes. The calculator returns the total surface area. For shapes that have them, it also gives the lateral area (the sides only) and the base area separately. That helps with jobs like labeling a can or painting the walls of a tank, which need just one part. The total is also converted to square meters and square feet.

Where it's used

Why this math matters outside the classroom:

  • Wrapping gifts. A gift box 30 cm by 20 cm by 10 cm needs 2 × (600 + 300 + 200) = 2,200 cm² of paper, before any overlap.
  • Can labels. A soup can 7.5 cm across and 11 cm tall needs a label of π × 7.5 × 11, about 259 cm².
  • Tent fabric. A square pyramid tent with a 2 m base and a 1.5 m slant height uses 4 × ½ × 2 × 1.5 = 6 m² of fabric for its sides.
  • Insulating a tank. Covering a cylindrical tank of radius 0.5 m and height 1.5 m, ends included, takes 2π(0.5)(1.5) + 2π(0.5)², about 6.28 m².
  • Painting a box. A cube-shaped storage box 3 ft on each edge has 6 × 3² = 54 square feet to paint.

Grade level and standards: Grades 6–8; Common Core State Standards for Mathematics 6.G.A.4, 7.G.B.6. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Select the shape: rectangular box, cube, cylinder, sphere, cone or rectangular pyramid.
  2. Select the unit your measurements are in, from millimeters to yards.
  3. Enter the sizes. Radius is half the width of a circle. Height is the straight up-and-down height, not the slanted length along a side.
  4. Read the total, then the lateral and base areas if you need only part of the surface.

What the inputs mean

Length
For a pyramid, the length of the rectangular base. Together with the width, it sets the base. The four triangular faces rise from its edges to a tip directly above the center.
Radius
For a cylinder, cone or sphere, the distance from the center of the circle to its edge. If you measured across the full width, halve it.
Height
The straight up-and-down height. For a cone or pyramid, it runs from the center of the base straight up to the tip. The calculator works out the slanted face heights itself.

Formula and method

Cube: SA = 6a²
Box: SA = 2(lw + lh + wh)
Cylinder: SA = 2πrh + 2πr²
Sphere: SA = 4πr²
Cone: l = √(r² + h²);  SA = πrl + πr²
Rectangular pyramid: SA = lw + l√(h² + (w ÷ 2)²) + w√(h² + (l ÷ 2)²)

SA is the surface area and a is the edge of a cube. For a box or pyramid, l, w and h are the length, width and height. For round shapes, r is the radius and h is the height. On the cone line, l is the slant height, measured along the sloping side. π (pi) is about 3.1416, and √ means square root.

Flat-faced solids are just the sum of their faces. A box has three pairs of matching rectangles. A rectangular pyramid has its base plus two pairs of triangles. Each triangle's height is the slant height, from the tip down to the middle of its base edge. It's found with the Pythagorean theorem, from the vertical height and half the other base side.

Curved solids use their unrolled shapes. The side of a cylinder unrolls into a rectangle whose length is the distance around the circle, 2πr. The side of a cone unrolls into a pie-slice shape whose area is π × radius × slant height. A sphere is the odd one out. Its whole curved skin, 4πr², equals four flat circles with the same radius as the ball.

Conversions square the length factor: 1 ft = 0.3048 m exactly, so 1 ft² = 0.09290304 m².

Worked example

A round tin is 4 cm in radius and 12 cm tall. How much sheet metal covers it, and how big a label wraps the side?

  1. Curved side: 2 × π × 4 × 12 ≈ 301.5929 cm². This is the label size.
  2. Each circular end: π × 4² ≈ 50.2655 cm².
  3. Total: 301.5929 + 2 × 50.2655 ≈ 402.1239 cm².
  4. In square meters: 402.1239 × 0.01² ≈ 0.0402 m².

Result: The tin's total surface is about 402.1239 cm², of which the side label covers about 301.5929 cm².

Understanding the result

Surface area grows with the square of size. Doubling every measurement multiplies it by four, while the volume grows eight times. That's why small objects have more surface for their size than large ones.

For coatings, use only the faces that will actually be covered. An open-topped tank, for example, needs the lateral area plus one base, not the full total.

Assumptions and limitations

  • Shapes are ideal: straight cylinders and cones (tip above the center of the base), and pyramids whose tip sits directly above the center of a rectangular base.
  • All measurements use the same unit.
  • US units use the international foot (0.3048 m).
  • Leaning (oblique) cylinders, cones and pyramids, hollow shapes and wall thickness aren't handled.
  • Open containers need adjusting by hand, by subtracting the missing face.
  • Real objects with seams, rims or rounded edges will differ slightly from the ideal figure.

Frequently asked questions

What is the difference between lateral area and total surface area?

Lateral area covers only the sides. That's the curved wall of a cylinder or cone, the four walls of a box, or the triangular faces of a pyramid. Total surface area adds the base or bases as well.

Why does the cone need a slant height?

The sloping surface of a cone is longer than its vertical height. The slant height l = √(r² + h²) measures along that surface, and the curved area is π × r × l. A cone with radius 3 and height 4 has a slant height of 5. Its total surface is 24π, about 75.4 square units.

How do I find the surface area of a box with no lid?

Work out the full box and subtract one length × width face. For a 4 × 3 × 2 box, the total is 52 square units and the open top is 12, leaving 40.

Can I use this to estimate paint?

Yes. Find the area of the faces you'll paint and multiply by the number of coats. Then divide by the coverage printed on the paint can. The paint calculator does this for rooms.

How this calculator is checked

Method: Standard surface-area formulas for right solids; slant heights from the Pythagorean theorem; international foot for conversions. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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