Surface Area Calculator
Find the total, side and base surface area of a box, cube, cylinder, cone, sphere, hemisphere, pyramid or triangular prism, with its volume.
Surface area is the total area of the outside of a solid. A box 4 in long, 3 in wide and 2 in high has a surface area of 52 square inches: 24 for the top and bottom and 28 for the four sides. Choose a shape, enter its measurements, and the calculator splits the total into side and base areas and adds the volume.
Results assume ideal shapes with closed ends (except the lateral figure) and are rounded to two decimals. The calculator does not account for material thickness, seams or overlap, so add a margin when buying paint, fabric or sheet stock.
Total surface area
52 square in
- Lateral (side) area
- 28 square in
- Area of both ends
- 24 square in
- Volume
- 24 cubic in
Embed this calculator on your site →
About the Surface Area Calculator
Surface area counts the outside of a solid in square units, the amount of paper to wrap it, paint to cover it or sheet metal to build it. Each shape unfolds into flat pieces. A cube has six equal squares, so a 3 in cube has 54 square inches. A closed cylinder unrolls into two circles and a rectangle as long as the circumference, so one with a 3 in radius and 5 in height comes to 150.8 square inches. A sphere has no flat faces and its area is 4 pi r squared, 314.16 square inches for a 5 in radius, and a closed hemisphere of the same radius adds its flat disk to half of that for 235.62. A triangular prism with 3, 4 and 5 in sides and a 10 in length has 120 square inches of rectangular sides and two 6 square inch triangles, 132 in all; the triangle's area comes from its three sides by Heron's formula, so you never need its height. The lateral area leaves out the bases, which is the figure to use when a shape is open at the ends.
Frequently asked questions
How do I find the surface area of a rectangular prism?+
Add the areas of its three pairs of faces: 2 times length times width, plus 2 times length times height, plus 2 times width times height. A tray 10 in by 6.5 in and 0.25 in deep has 130 square inches of top and bottom and 8.25 of edges, 138.25 in total.
What is the surface area of a cone?+
The base circle, pi r squared, plus the side, pi times r times the slant height. The slant is the square root of r squared plus h squared, so a cone with a 3 in radius and 4 in height has a 5 in slant, 47.12 square inches of side and 28.27 of base, 75.4 in total.
How do I work out a pyramid's surface area?+
Add the base to the four triangular faces, each half its base edge times its slant height. A pyramid on a 6 in square base, 4 in tall, has slant heights of 5 in, so 60 square inches of faces and a 36 square inch base, 96 in all. A rectangular base gives two different slant heights, and the calculator shows both.
When should I use lateral area instead of total area?+
When the ends are open or not being covered. The walls of a room 12 ft by 10 ft with an 8 ft ceiling are a lateral area of 352 square feet; counting the floor and ceiling as well would make it 592.
Formulas: OpenStax, Prealgebra 2e, 9.6; Weisstein EW, MathWorld: Cone, Spherical Cap, Pyramid, Heron's Formula.
Embed this calculator
Free to use on your own site. Paste this snippet where you want the surface area calculator to appear — it resizes itself automatically.
<iframe
src="https://manytools.co/embed/surface-area-calculator"
title="Surface Area Calculator by ManyTools"
data-manytools="surface-area-calculator"
width="100%"
height="640"
loading="lazy"
style="border:0;width:100%;max-width:720px"></iframe>
<script>
(function () {
window.addEventListener("message", function (e) {
if (e.origin !== "https://manytools.co") return;
var d = e.data || {};
if (d.type !== "manytools:embed:height" || d.slug !== "surface-area-calculator") return;
var f = document.querySelector('iframe[data-manytools="surface-area-calculator"]');
if (f && d.height) f.style.height = d.height + "px";
});
})();
</script><a href="https://manytools.co/math/surface-area-calculator">Surface Area Calculator by ManyTools</a>