Square Inches Calculator

What a square inch measures

A square inch is a square that measures one inch on every side. It describes area, meaning how much flat surface something covers, not how long it is. A dollar bill laid flat covers 16.03 square inches, and a standard sheet of letter paper covers 93.5.

The unit is exact because the inch is exact. One inch is 0.0254 meter by the 1959 agreement on the yard and pound, so one square inch is 0.0254 x 0.0254 = 0.00064516 square meter, which is 6.4516 square centimeters. The NIST Guide to the SI, Appendix B.9 lists the square inch as 6.4516 E-04 square meters and prints it as an exact factor.

Three numbers cover most of the arithmetic on this page:

• 144 square inches in a square foot, because 12 x 12 = 144
• 1,296 square inches in a square yard, because 36 x 36 = 1,296
• 6.4516 square centimeters in a square inch

That is why square inches suit small surfaces and square feet suit rooms. A panel 20 inches by 20 inches covers 400 square inches, which sounds large until you divide by 144 and get 2.7778 square feet. It is the same area described two ways.

Length times width: the arithmetic for square inches

For a rectangle, area in square inches is length times width with both sides measured in inches. A shelf 30 inches long and 11 inches deep covers 30 x 11 = 330 square inches. A 12 inch tile covers 12 x 12 = 144 square inches, which is exactly one square foot, and that is why the price per tile and the price per square foot match so neatly at that size.

A circle uses 3.1416 x radius^2. A 10 inch round pan has a radius of 5 inches, so it covers 3.1416 x 5^2 = 78.54 square inches. If you only know the diameter, halve it before you square it. A 12 inch pizza pan covers 113.1 square inches and a 14 inch pan covers 153.94, so two extra inches of pan buy about 36 percent more surface.

A triangle takes half of base times height. A gable end 24 inches wide and 18 inches tall covers 24 x 18 / 2 = 216 square inches. Measure the height square to the base, not along the sloped edge, or the answer comes out too large.

Small measuring errors grow once they are squared. An eighth of an inch missing from a 20 inch side costs about 2.5 square inches on that side. The same eighth missing from both sides of a 40 inch panel costs close to 10 square inches, which is a real gap when you are ordering glass or sheet metal.

Square inches to square feet, centimeters and meters

Converting square inches is a single division or multiplication, and the number to use depends on the unit you want. To go to square feet, divide by 144. To go to square centimeters, multiply by 6.4516. To go to square meters, multiply by 0.00064516. To go to square yards, divide by 1,296.

Work from the number you have in hand. If a label says 400 square inches and you need square feet for a flooring order, divide once: 400 / 144 = 2.7778 square feet. If a plan gives 2 square feet and you need square inches, multiply: 2 x 144 = 288 square inches. Multiplying when you meant to divide is the most common error in this family of conversions, and it is easy to catch because the answer moves in the wrong direction.

Keep the unit attached to the number while you work. Writing square inches as sq in and square feet as sq ft avoids the slip where 2 square feet turns into 2 feet and the whole calculation drifts into a length.

Furnace filters: square inches decide airflow

Furnace filters and return grilles are sold by nominal size in inches, and the face area is length times width. A 20 by 25 inch filter has 500 square inches of face area, or 3.4722 square feet. That area sets how fast air moves through the filter, and the speed is what decides whether a high MERV filter chokes the blower.

The formula in the Department of Energy's air conditioner diagnostics guide is filter velocity = tons x 57,600 / (L x W), with L and W in inches. A 2 ton system behind a 20 by 25 filter runs at 2 x 57,600 / 500 = 230.4 feet per minute. The same guide suggests keeping velocity at or under 300 feet per minute.

Put a 3 ton system, roughly 1,200 cubic feet per minute, behind a 20 by 20 filter and the numbers turn ugly: 1,200 x 144 / 400 = 432 feet per minute. That filter is too small for the blower. To stay at 300 feet per minute the same system needs 1,200 x 144 / 300 = 576 square inches, which is why an installer steps up to a 20 by 25 or adds a second return.

Watch the difference between nominal and actual size. A filter sold as 20 by 20 often measures 19.5 by 19.5 in the box, which is 380.25 square inches, about 5 percent less face area than the label suggests. The EPA page on MERV ratings explains what the filter is trapping; the square inches explain whether the duct can feed it without starving the blower.

Pans, sheets and countertop appliances

Baking recipes scale by area, and square inches is the number to compare. A 9 by 13 inch pan covers 117 square inches. An 8 by 8 inch pan covers 64. The rectangle holds 117 / 64 = 1.83 times as much batter, so a recipe written for the square pan needs about 83 percent more batter in the rectangle, or the same batter sits a little over half as deep.

A half sheet pan is 13 by 18 inches, or 234 square inches. A quarter sheet is 9 by 13, or 117. A 9 inch round cake pan covers 3.1416 x 4.5^2 = 63.62 square inches, close to the 8 by 8 square, which is why layer cake recipes swap between those two without much trouble. A 10 inch round pan covers 78.54 square inches, about 23 percent more than the 9 inch.

The same arithmetic sizes air fryer baskets, toaster oven racks and microwave turntables. A 12 by 12 inch basket has 144 square inches of cooking surface, and a 9 by 9 inch basket has 81, so the larger one fits close to twice the food in a single layer. A 10 inch microwave turntable needs a plate no wider than 10 inches, which is a limit on diameter rather than area.

Paper, photos, screens and tile

Print sizes are quoted in inches but priced by area more often than people notice. A 4 by 6 inch print is 24 square inches, a 5 by 7 is 35, an 8 by 10 is 80 and a 16 by 20 is 320. The large print has 320 / 24 = 13.3 times the area of the small one even though its long side is only 3.3 times as long, which is why the frame costs so much more.

Paper follows the same rule. US Letter is 8.5 by 11 inches, or 93.5 square inches. Legal is 8.5 by 14, or 119 square inches, 27 percent more paper. Tabloid is 11 by 17, or 187 square inches, exactly twice Letter.

Screens are sold by diagonal, which is a length and not an area. A 15 inch laptop screen with a 16:10 shape measures about 12.72 by 7.95 inches, or 101.12 square inches. A 6.1 inch phone with a 19.5:9 shape measures about 5.54 by 2.56 inches, or 14.16 square inches. Compare two screens by multiplying width by height, never by comparing the diagonal numbers on the box.

Tile is the easiest case of the group. A 12 by 12 tile is 144 square inches, one square foot, so a 100 square foot room needs 100 tiles plus waste. A 6 by 6 tile is 36 square inches, so the same room needs 400 of them, and a 4 by 4 tile is 16 square inches, or 900 tiles. Buying by the box, add 10 percent for cuts and breakage before you divide by the area on the box.

Cost per square inch, and the mistakes that cost money

Price per square inch is the fastest way to compare materials sold in different sizes. Divide the price by the area. A piece that costs $40 and covers 400 square inches works out to 40 / 400 = 0.10, so it is $0.10 per square inch or 0.10 x 144 = $14.40 per square foot. A piece that costs $15 and covers 120 square inches is $0.125 per square inch, or $18.00 per square foot, so the cheaper sticker is the more expensive material.

Three mistakes show up again and again. The first is forgetting to square the unit: a square 2 feet on a side is 4 square feet, not 2, and a 24 by 24 inch panel is 576 square inches, not 48. The second is mixing units inside one multiplication, such as 20 inches times 2 feet. Convert both sides to inches first, so 20 x 24 = 480 square inches.

The third is trusting a nominal size. Lumber, filters and pans are all sold by nominal dimensions that differ from the measured ones. A 2 by 4 measures 1.5 by 3.5 inches, or 5.25 square inches of end grain, not the 8 square inches the name suggests.

Round at the end, not in the middle. Carrying 400 square inches through a division by 144 gives 2.7778 square feet, and rounding that to 2.8 is fine for a shopping list as long as you multiply by the price afterwards rather than before.

One last check that catches most errors: estimate the answer from square feet first. A 400 square inch area is a bit under 3 square feet, because 3 square feet is 432 square inches. If your calculator says 27.8 square feet, a decimal point moved and you can see it before the order goes out.