Total against curved area
Total surface area covers every outside face, including the ends. The curved or side area leaves out the flat ends, which is what you need for a label, a wrap or a coat of paint on the sides only.
For a box the total is 2 x (lw + lh + wh) and the sides are 2 x (l + w) x h. For a cylinder the total is 2 x pi x r x (r + h) and the curved part is 2 x pi x r x h.
Worked example
A box 30 cm by 20 cm by 15 cm has a total surface area of 2 x (600 + 450 + 300) = 2,700 cm².
That is 0.27 m². Its side area, without the top and bottom, is 2 x (30 + 20) x 15 = 1,500 cm², or 0.15 m².
Why the sphere has no separate curved figure
A sphere has no flat faces, so its total and curved areas are the same: 4 x pi x radius squared.
For a cone, the total adds the circular base to the curved surface. The curved part needs the slant height, which the calculator works out from the radius and height.
Inputs for the surface area calculator
Shape
Pick the solid. The measurement boxes change to the dimensions that shape needs.
Length, width and height
The three sides of a box, at right angles to each other.
Radius and height
Used by the cylinder, cone and sphere. The radius is half the width across the widest point.
Measurement unit
The unit your measurements are in. The answer is given in square metres.
CALCULATOR QUESTIONS
Surface area calculator questions
How do I work out the surface area of a box?
Add the areas of the three pairs of faces: 2 x (length x width + length x height + width x height).
What is curved surface area?
The area of the sides only, without the flat ends. For a cylinder it is 2 x pi x radius x height.
Why does a sphere show the same figure twice?
A sphere has no flat faces, so its total surface area and its curved area are the same number.
Does surface area help me buy paint?
Yes, if you divide by the coverage printed on the tin. This page gives the area; the number of coats is your own choice.