Length and angle unit converter

What the converter computes

Enter a value, the unit it is in and the unit you want. The result is the value multiplied by one conversion factor. The converter prints that factor as a sentence, such as 1 in = 25.4 mm, so you can check it against your own reference.

The rounded figure uses the number of significant figures you choose. When rounding drops a digit, the full value appears underneath it. A conversion never loses a digit without telling you.

Where the factors come from

The international inch has been defined as exactly 25.4 mm since 1959. NIST SP 811 lists the inch, the foot and the mil with exact factors. The converter uses those definitions and nothing measured:

• 1 in = 25.4 mm, exactly.
• 1 ft = 12 in = 304.8 mm, exactly.
• 1 thou (also called a mil) = 0.001 in = 25.4 µm, exactly. A mil is not a millimetre.
• 1 m = 1000 mm, 1 cm = 10 mm and 1 µm = 0.001 mm.

For angles, 1° = 60′ (arcminutes), 1′ = 60″ (arcseconds) and 1 grad, also called a gon, = 0.9°. The radian is the exception: 1 rad = 180°/π. Because π is irrational, no conversion between radians and another unit has an exact decimal result.

How the arithmetic avoids drift

Computers store most decimals, such as 0.1 or 25.4, as close binary approximations. Converting with those approximations can leave a stray digit in the fifteenth place. The converter treats the value you typed as an exact decimal instead. Every length unit is a whole number of nanometres, and every angle unit except the radian is a whole number of arcseconds, so each factor is an exact fraction. The tool multiplies and divides those whole numbers exactly, then rounds once, for display.

When the division does not end, as with millimetres to inches, the full value is the closest double-precision number to the exact result. The tool says so next to it. Results in radians are computed in double precision, with π to about 16 significant digits.

Significant figures and rounding

Rounding goes to the nearest value, and a tie rounds away from zero. It is applied to the decimal value, never to its binary approximation. Trailing zeros are kept because they are significant: 25.4 mm at six significant figures shows as 25.4000. When plain notation would hide which zeros are significant, as with 12 300 at three figures, the result is shown as 1.23e+4.

A converted value should not claim more precision than the original. NIST SP 811 gives guidance on rounding converted values. A dimension of 0.50 in converts to 12.7 mm, and writing it as 12.700 mm implies a precision the original never stated.

Worked example

Limitations

• Length and plane angle only. No area, volume, mass, force, pressure or temperature.
• Inputs take a decimal point, not a decimal comma, and at most 15 significant digits. Values a double cannot hold, such as 1e400, are refused with a message.
• The converter does not convert a tolerance on its own. Convert each limit, then round each one so the band stays inside the original limits.
• Survey feet and other non-international definitions are not included.

When to involve a qualified engineer

Converting a toleranced dimension between unit systems changes how it is rounded. Rounding a limit outward can accept parts that the original drawing rejects. When a converted drawing will be used to make or inspect parts, have the engineer who owns the drawing approve the converted limits and their rounding.