3 Inches to Centimeters

Three inches is 7.62 centimeters, and the decimal stops there

Three inches is 3 x 2.54 = 7.62 cm exactly. Nothing repeats and nothing rounds, because the inch is defined as 25.4 mm. The same length is 76.2 mm, 0.0762 m, 0.25 ft and 0.0833333 yd.

NIST Special Publication 811 lists 1 in = 2.54 cm exactly (NIST, 2008), and the BIPM SI brochure carries the same value through the metre. The number comes from the 1959 agreement between the US, the UK, Canada, Australia, New Zealand and South Africa, which fixed the international yard at 0.9144 m and made the inch 1/36 of that yard.

Rounding is where the trouble starts. A metric drawing that writes 76 mm instead of 76.2 mm is 0.2 mm under the true size, and a 3 in bearing pressed into a 76 mm bore sits 0.2 mm loose. Across three stacked parts the same shortcut adds 0.6 mm, which is enough to leave a visible step in a frame.

Four pieces of 3 in stock make exactly 1 ft, because 3 in is a quarter of 12 in. That is the one imperial split of a foot that lands on a whole centimeter-free number in both systems: 12 in is 30.48 cm, and each quarter is 7.62 cm.

A 3 inch hockey puck and a 3 inch shotshell

Some objects are defined in inches by rule, and a 3 in size is part of the specification rather than a measurement. An ice hockey puck is 3 in across and 1 in thick, which is 7.62 cm across and 2.54 cm thick, with a circumference of pi x 7.62 = 23.94 cm and a face area of 45.6 cm².

Shotgun shells are named by the length of the fired hull. A 3 in shell is 76.2 mm long, a 2 3/4 in shell is 69.85 mm, and the 6.35 mm difference is what decides whether a 3 in load fits a given gun. A 3 in chamber accepts the shorter shell as well, while a 2 3/4 in chamber does not close on a 3 in shell.

Makers of both items publish inches and let the metric figure follow, so a European rulebook prints 76.2 mm for the shell and 76 mm for the chamber, and the 0.2 mm gap is treated as tolerance rather than error. That habit is why a metric drawing of a 3 in part should carry 76.2 and not 76.

Screens, photo prints and a 3 inch diagonal

A 3 in diagonal is 7.62 cm, which is a small display by current standards. A 6.1 in phone has a 15.494 cm diagonal, so 7.62 cm covers 49.18 percent of it. A 3 in screen on a dash camera or a door viewer sits in that range, and the inch figure on the box is the diagonal, never the width.

Photo printing keeps the inch label and adds the metric size on the same envelope. A 3 by 5 in print is 7.62 by 12.7 cm, and at 300 dpi it is 900 by 1500 px. A 3 by 3 in square print is 7.62 by 7.62 cm, or 900 by 900 px, which is the size a passport photo lab quotes in both systems.

Bezels and margins behave the same way. A 3 in bezel around a 6.1 in screen would be 7.62 cm on each side, which is wider than the phone, so the number is only plausible on a tablet or a monitor. Reading the spec sheet in one unit and the tape in the other is how a 7.62 cm border becomes a 76 mm one and a frame no longer closes.

Screws, bolts and hole saws: 3 in is 76.2 mm on the shank

A 3 in wood screw has a 76.2 mm shank, and the gauge number in front of it, such as 10 or 12, sets the diameter rather than the length. Buy the same screw in a metric market and the packet says 76 mm, which is 0.2 mm short and does not matter for a screw, since the length is measured to the tip and the thread bites into wood.

Hole saws and Forstner bits are less forgiving. A 3 in hole saw cuts a 76.2 mm hole, and the nearest metric saw is 76 mm, which leaves the hole 0.2 mm small. For a pipe passing through a floor that clearance is nothing; for a bushing pressed into the hole it is the difference between a fit and a rattle.

Bolts mix the two systems in one line. A 3 in bolt has 76.2 mm of shank under the head, and its thread is inch series, such as 3/8-16 or 1/2-13, so the nut is bought in inches even when the drawing is metric. Metric bolts are named by a whole millimeter thread diameter, so no metric size equals 76.2 mm, and the drawing keeps the inch thread series while converting only the length.

Drill sizes follow the same logic. A 3 in hole needs a pilot, and the pilot is chosen from the screw gauge, not from the length. That separation is why a 3 in screw and a 76 mm screw are the same part while a 3 in hole and a 76 mm hole are not.

Pipe: NPS 3 measures 8.89 cm outside, not 7.62

The 3 in on a pipe is a nominal label, so NPS 3 does not measure 7.62 cm anywhere. Schedule 40 NPS 3 pipe has a 3.500 in outside diameter, which is 8.89 cm, and a 3.068 in inside diameter, which is 7.79 cm. The wall is 0.216 in, or 0.55 cm, and the 3 in in the name points at the old iron pipe bore.

Schedule 80 keeps the same outside diameter and thickens the wall, so the inside drops to 2.900 in, or 7.37 cm. The outside stays 8.89 cm because the fittings and the thread are sized on the outside, and that is why a schedule change does not change the coupling.

Copper tube is sized by outside diameter instead. Three inch type L copper measures 3.125 in outside, or 7.94 cm, with a 2.945 in inside, or 7.48 cm. The metric label for the same pipe family is DN 80, and a DN 80 flange bolts to an NPS 3 flange because the bolt circle and pressure class match, not because any diameter converts to 7.62 cm.

Three inches of rain on a 1,000 square foot roof

Three inches of rain is 7.62 cm of depth. On a 1,000 ft² roof, which is 92.903 m², that is 92.903 x 0.0762 = 7.079 m³, or 7,079.2 L. In gallons the same catch is 1,870.1 gal, since one cubic foot holds 7.48052 gal and the roof takes 250 ft³.

Rain gauges report inches in the US and millimeters almost everywhere else, so 3 in reads 76.2 mm on a metric gauge. A storm that drops 3 in in one hour is running at 76.2 mm per hour, which is a rate that overwhelms a residential gutter and sends water over the fascia. The National Weather Service publishes rainfall rates and flood thresholds in both units, and a 3 in total in 24 hours is a soaking rather than a flood in most of the country.

Snow is reported as water equivalent. At the common 10 to 1 ratio, 3 in of water is about 30 in of snow, and 3 in of snow is only 0.3 in of water, or 0.762 cm. The inch to centimeter conversion applies to the melted depth, never to the depth in the yard.

Irrigation uses the same figure from the other direction. A sprinkler putting out 0.5 in per hour delivers 1.27 cm per hour, so replacing a 3 in deficit takes six hours of run time. A drip line rated in liters per hour is sized from the same 7,079 L total, divided by the hours available.

Fractions, square inches and cubic inches at 3 in

Fractional inches convert one step at a time, and 3 in is a tidy 48 sixteenths. One sixteenth is 0.0625 in, which is 1.5875 mm, so a tolerance of plus or minus 1/16 in is plus or minus 1.59 mm. A tape marked in sixteenths and a rule marked in millimeters describe the same points, and every value below comes from the single factor of 2.54.

Area and volume take the factor twice and three times. Three square inches is 3 x 6.4516 = 19.3548 cm², and three cubic inches is 3 x 16.387064 = 49.1612 cm³, which is 49.16 mL. A 3 in cube holds 49.16 mL, and a 3 in pipe bore holds pi x 3.81 squared x 1 = 45.6 cm³ per centimeter of length.

The 76.2 mm checkpoint is worth memorizing. It is the metric face of 3 in, it is the length of a 3 in shell, and it is the bore of a 3 in hole saw. A drawing that shows 76 mm is 0.2 mm short of all three, which is harmless on a shell, marginal on a hole and wrong on a press fit.