What is the difference between total and lateral surface area?

Lateral area is the curved or sloping side alone; total area adds the flat ends. A label wrapping a tin needs the lateral area, and making the tin needs the total. On a short wide cylinder the two differ by more than half, which is why the distinction is worth printing rather than assuming.

Why does a cone need a slant height?

Because the surface runs along the slope, not straight up. The slant is the hypotenuse of the radius and the vertical height, so a cone 3 ft across and 4 ft tall has a slant of 4.27 ft. Using 4 instead understates the curved surface by about 7%, and the steeper the cone the worse it gets.

How much paint will I need?

A gallon covers roughly 350 square feet on a smooth surface for one coat, which is the figure above. Rough masonry drinks a third more, and two coats over a colour change is the normal case — so double the figure before buying unless the surface is sealed and the colour is close.

Is surface area proportional to volume?

No, and the gap is why small things cool faster. Double every dimension and the surface area goes up four times while the volume goes up eight, so the area per unit of volume halves. It is the reason a mouse eats more per gram than an elephant and a small pipe loses heat faster per liter carried.

Surface Area Calculator

With length 4 ft, width 2 ft, depth 3 ft, surface area comes to 52.000 sq ft — surface area. It is reached in 6 steps, the last of which is shape_box ? s_box : shape_cube ? s_cube : shape_cylinder ? s_cylinder : shape_sphere ? s_sphere : shape_cone ? s_cone : shape_pyramid ? s_pyramid : s_capsule, and each one is printed on the page with its numbers filled in. The formula is the one published by Wolfram MathWorld, not an approximation fitted to it.

Surface area of a box, cube, cylinder, sphere, cone, pyramid, capsule or ellipsoid, with the lateral area given separately from the ends.

Formula and sources checked 27 August 2026 · How we check

Shape Rectangular box, Length 4 ft, Width 2 ft, Depth 3 ft

52.000 sq ft

Surface area for the example below. Editing a field recomputes the calculator below; this figure holds the answer the page was loaded with.

It is written into the HTML rather than drawn by a script, so a search engine reading this page without running JavaScript still finds an answer.

ShapeLengthWidthDepth

Surface area

52.000 sq ft

4.831 square meters

Cone slant height: sqrt(pow(3 / 2, 2) + pow(4, 2))4.272 ft
Pyramid slant height: sqrt(pow(4 / 2, 2) + pow(6, 2))6.325 ft
Total surface area: 52 sq ft
Lateral area, without the ends: 52 sq ft
In square meters: 52 * 0.0929034.831 m²
Gallons of paint for one coat: 52 / 3500.149 gal

Several at once

A job is rarely one of anything. Work out the first, add it, change the figures and add the next — the list keeps what each line was, and totals them.

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Worked example

A box 4 by 2 by 3 has three pairs of faces — 8, 12 and 6 square feet — so 52 square feet in total. At 350 square feet to the gallon that is 0.149 gallons of paint for one coat, which is why a quart is the sensible purchase.

How to work it out yourself

1.Pick the shape and measure the outside. Surface area is about the skin, so wall thickness does not enter it.
2.For a cone or a pyramid, the calculator works out the slant height itself from the vertical height. Measuring along the slope and entering that as the height doubles the error.
3.Read the lateral line if the ends do not need covering — a label around a tin, insulation on a duct, or the sides of a silo.

The formula

Cone slant heightsqrt(pow(3 / 2, 2) + pow(4, 2))
Pyramid slant heightsqrt(pow(4 / 2, 2) + pow(6, 2))
Total surface area
Lateral area, without the ends
In square meters52 * 0.092903
Gallons of paint for one coat52 / 350

Source: Wolfram MathWorld — solid geometry

Questions people actually ask

What is the difference between total and lateral surface area?: Lateral area is the curved or sloping side alone; total area adds the flat ends. A label wrapping a tin needs the lateral area, and making the tin needs the total. On a short wide cylinder the two differ by more than half, which is why the distinction is worth printing rather than assuming.
Why does a cone need a slant height?: Because the surface runs along the slope, not straight up. The slant is the hypotenuse of the radius and the vertical height, so a cone 3 ft across and 4 ft tall has a slant of 4.27 ft. Using 4 instead understates the curved surface by about 7%, and the steeper the cone the worse it gets.
How much paint will I need?: A gallon covers roughly 350 square feet on a smooth surface for one coat, which is the figure above. Rough masonry drinks a third more, and two coats over a colour change is the normal case — so double the figure before buying unless the surface is sealed and the colour is close.
Is surface area proportional to volume?: No, and the gap is why small things cool faster. Double every dimension and the surface area goes up four times while the volume goes up eight, so the area per unit of volume halves. It is the reason a mouse eats more per gram than an elephant and a small pipe loses heat faster per liter carried.

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