Fraction to Decimal Conversion Chart for Wrenches & Sockets
Fraction to Decimal & mm
Direct Answer
To convert a fraction to a decimal, divide the numerator by the denominator. 7/8 as a decimal equals 7 ÷ 8, or 0.875 inches. In millimeters, that's 22.225mm, and the closest stocked metric socket is 22mm.
This conversion comes up constantly with tools, since sockets and wrenches are stamped in fractional inches (3/8, 1/2, 5/8) but most calculators, spreadsheets, and CAD software need a decimal input. This page covers the full fraction-to-decimal table from 1/64 inch to 2 inches, the most common wrench fractions with their millimeter equivalents, and how to read a worn or unmarked fractional tool.
Full Fraction to Decimal Table (1/64" to 2")
| Fraction | Decimal | mm |
|---|---|---|
| 1/64" | 0.0156" | 0.397mm |
| 1/32" | 0.0313" | 0.794mm |
| 3/64" | 0.0469" | 1.191mm |
| 1/16" | 0.0625" | 1.587mm |
| 5/64" | 0.0781" | 1.984mm |
| 3/32" | 0.0938" | 2.381mm |
| 7/64" | 0.1094" | 2.778mm |
| 1/8" | 0.1250" | 3.175mm |
| 9/64" | 0.1406" | 3.572mm |
| 5/32" | 0.1563" | 3.969mm |
| 11/64" | 0.1719" | 4.366mm |
| 3/16" | 0.1875" | 4.762mm |
| 13/64" | 0.2031" | 5.159mm |
| 7/32" | 0.2188" | 5.556mm |
| 15/64" | 0.2344" | 5.953mm |
| 1/4" | 0.2500" | 6.350mm |
| 17/64" | 0.2656" | 6.747mm |
| 9/32" | 0.2813" | 7.144mm |
| 19/64" | 0.2969" | 7.541mm |
| 5/16" | 0.3125" | 7.938mm |
| 21/64" | 0.3281" | 8.334mm |
| 11/32" | 0.3438" | 8.731mm |
| 23/64" | 0.3594" | 9.128mm |
| 3/8" | 0.3750" | 9.525mm |
| 25/64" | 0.3906" | 9.922mm |
| 13/32" | 0.4063" | 10.319mm |
| 27/64" | 0.4219" | 10.716mm |
| 7/16" | 0.4375" | 11.112mm |
| 29/64" | 0.4531" | 11.509mm |
| 15/32" | 0.4688" | 11.906mm |
| 31/64" | 0.4844" | 12.303mm |
| 1/2" | 0.5000" | 12.700mm |
| 33/64" | 0.5156" | 13.097mm |
| 17/32" | 0.5313" | 13.494mm |
| 35/64" | 0.5469" | 13.891mm |
| 9/16" | 0.5625" | 14.287mm |
| 37/64" | 0.5781" | 14.684mm |
| 19/32" | 0.5938" | 15.081mm |
| 39/64" | 0.6094" | 15.478mm |
| 5/8" | 0.6250" | 15.875mm |
| 41/64" | 0.6406" | 16.272mm |
| 21/32" | 0.6563" | 16.669mm |
| 43/64" | 0.6719" | 17.066mm |
| 11/16" | 0.6875" | 17.462mm |
| 45/64" | 0.7031" | 17.859mm |
| 23/32" | 0.7188" | 18.256mm |
| 47/64" | 0.7344" | 18.653mm |
| 3/4" | 0.7500" | 19.050mm |
| 49/64" | 0.7656" | 19.447mm |
| 25/32" | 0.7813" | 19.844mm |
| 51/64" | 0.7969" | 20.241mm |
| 13/16" | 0.8125" | 20.637mm |
| 53/64" | 0.8281" | 21.034mm |
| 27/32" | 0.8438" | 21.431mm |
| 55/64" | 0.8594" | 21.828mm |
| 7/8" | 0.8750" | 22.225mm |
| 57/64" | 0.8906" | 22.622mm |
| 29/32" | 0.9063" | 23.019mm |
| 59/64" | 0.9219" | 23.416mm |
| 15/16" | 0.9375" | 23.813mm |
| 61/64" | 0.9531" | 24.209mm |
| 31/32" | 0.9688" | 24.606mm |
| 63/64" | 0.9844" | 25.003mm |
| 1" | 1.0000" | 25.400mm |
| 1-1/64" | 1.0156" | 25.797mm |
| 1-1/32" | 1.0313" | 26.194mm |
| 1-3/64" | 1.0469" | 26.591mm |
| 1-1/16" | 1.0625" | 26.987mm |
| 1-5/64" | 1.0781" | 27.384mm |
| 1-3/32" | 1.0938" | 27.781mm |
| 1-7/64" | 1.1094" | 28.178mm |
| 1-1/8" | 1.1250" | 28.575mm |
| 1-9/64" | 1.1406" | 28.972mm |
| 1-5/32" | 1.1563" | 29.369mm |
| 1-11/64" | 1.1719" | 29.766mm |
| 1-3/16" | 1.1875" | 30.162mm |
| 1-13/64" | 1.2031" | 30.559mm |
| 1-7/32" | 1.2188" | 30.956mm |
| 1-15/64" | 1.2344" | 31.353mm |
| 1-1/4" | 1.2500" | 31.750mm |
| 1-17/64" | 1.2656" | 32.147mm |
| 1-9/32" | 1.2813" | 32.544mm |
| 1-19/64" | 1.2969" | 32.941mm |
| 1-5/16" | 1.3125" | 33.337mm |
| 1-21/64" | 1.3281" | 33.734mm |
| 1-11/32" | 1.3438" | 34.131mm |
| 1-23/64" | 1.3594" | 34.528mm |
| 1-3/8" | 1.3750" | 34.925mm |
| 1-25/64" | 1.3906" | 35.322mm |
| 1-13/32" | 1.4063" | 35.719mm |
| 1-27/64" | 1.4219" | 36.116mm |
| 1-7/16" | 1.4375" | 36.512mm |
| 1-29/64" | 1.4531" | 36.909mm |
| 1-15/32" | 1.4688" | 37.306mm |
| 1-31/64" | 1.4844" | 37.703mm |
| 1-1/2" | 1.5000" | 38.100mm |
| 1-33/64" | 1.5156" | 38.497mm |
| 1-17/32" | 1.5313" | 38.894mm |
| 1-35/64" | 1.5469" | 39.291mm |
| 1-9/16" | 1.5625" | 39.688mm |
| 1-37/64" | 1.5781" | 40.084mm |
| 1-19/32" | 1.5938" | 40.481mm |
| 1-39/64" | 1.6094" | 40.878mm |
| 1-5/8" | 1.6250" | 41.275mm |
| 1-41/64" | 1.6406" | 41.672mm |
| 1-21/32" | 1.6563" | 42.069mm |
| 1-43/64" | 1.6719" | 42.466mm |
| 1-11/16" | 1.6875" | 42.862mm |
| 1-45/64" | 1.7031" | 43.259mm |
| 1-23/32" | 1.7188" | 43.656mm |
| 1-47/64" | 1.7344" | 44.053mm |
| 1-3/4" | 1.7500" | 44.450mm |
| 1-49/64" | 1.7656" | 44.847mm |
| 1-25/32" | 1.7813" | 45.244mm |
| 1-51/64" | 1.7969" | 45.641mm |
| 1-13/16" | 1.8125" | 46.037mm |
| 1-53/64" | 1.8281" | 46.434mm |
| 1-27/32" | 1.8438" | 46.831mm |
| 1-55/64" | 1.8594" | 47.228mm |
| 1-7/8" | 1.8750" | 47.625mm |
| 1-57/64" | 1.8906" | 48.022mm |
| 1-29/32" | 1.9063" | 48.419mm |
| 1-59/64" | 1.9219" | 48.816mm |
| 1-15/16" | 1.9375" | 49.212mm |
| 1-61/64" | 1.9531" | 49.609mm |
| 1-31/32" | 1.9688" | 50.006mm |
| 1-63/64" | 1.9844" | 50.403mm |
| 2" | 2.0000" | 50.800mm |
Most Common Wrench Fractions
- 1/4" = 0.2500" = 6.35mm
- 5/16" = 0.3125" = 7.94mm
- 3/8" = 0.3750" = 9.52mm
- 7/16" = 0.4375" = 11.11mm
- 1/2" = 0.5000" = 12.70mm
- 9/16" = 0.5625" = 14.29mm
- 5/8" = 0.6250" = 15.88mm
- 11/16" = 0.6875" = 17.46mm
- 3/4" = 0.7500" = 19.05mm
- 7/8" = 0.8750" = 22.22mm
- 15/16" = 0.9375" = 23.81mm
- 1" = 1.0000" = 25.40mm
7/8 as a Decimal
7/8 equals 0.875 inches, or 22.225mm. The closest metric socket is 22mm, a difference of 0.009 inch, which counts as use-with-caution rather than a highly interchangeable match. For torque-critical fasteners, fit a proper 7/8 inch SAE socket rather than substituting the 22mm metric size.
Converting Mixed Numbers to Decimal
A mixed number, such as 1-1/2 inch, converts in two steps. First, convert the fractional part alone: 1 ÷ 2 equals 0.5. Second, add the whole number back: 1 + 0.5 equals 1.5 inches. The same method applies to any size in this format, such as 1-3/16 inch, where 3 ÷ 16 equals 0.1875, giving a total of 1.1875 inches.
Why Tool Fractions Use Powers of Two
Wrench and socket sizes step in halves, quarters, eighths, sixteenths, thirty-seconds, and sixty-fourths of an inch because that's how a ruler or tape measure has historically subdivided the inch: fold it in half, then in half again. A denominator like 64 isn't an arbitrary choice; it's the sixth halving of a single inch, which is why nearly every fractional tool size in common use reduces to a denominator that's a power of two.
How to Read Fractional Wrench Sizes
Fractional sizes are usually stamped directly on the side of the socket or wrench, such as 3/8, 1/2, 5/8, or 3/4. That fraction is the size in inches across the flats of the hex opening, the same measurement metric sizes give in millimeters. When the marking is worn away, measure the opening with calipers and match the decimal reading to the table above.
Fraction Conversion for Socket Size Matching
When matching an SAE socket to a metric fastener, convert the metric value to a decimal inch first using the mm to inches reference, then find the closest fraction on the table here. A difference under 0.005 inch is a safe substitute for most work; a difference over 0.015 inch risks rounding the fastener and should be avoided.
Fraction to Decimal FAQ
What is 7/8 as a decimal?
7/8 equals 0.875 inches. Divide the numerator, 7, by the denominator, 8, to get the decimal value: 7 ÷ 8 = 0.875.
How do I convert a mixed number fraction to decimal?
Convert the fractional part first, then add the whole number. For 1-1/2 inch, 1 ÷ 2 = 0.5, so 1-1/2 equals 1 + 0.5, or 1.5 inches.
What decimal is closest to a 9/16 inch socket?
9/16 inch equals 0.5625 inches exactly. In millimeters, that's 14.29mm, closest to a 14mm metric socket.
Why do wrench and socket fractions use denominators like 8, 16, 32, and 64?
Those denominators are all powers of two, which is how inch-based measuring tools have historically subdivided the inch: half, then half again, and so on. A ruler, tape measure, or socket set marked in 1/64 inch increments is simply the result of dividing an inch in half six times over.
How accurate do I need to be when converting a fraction to decimal?
For most socket and wrench work, four decimal places (such as 0.4375 inch) is more than enough precision. Machining and other tight-tolerance work sometimes needs a fifth decimal place, but hand tool sizing never does.
Can I convert a decimal back into a fraction?
Yes. Multiply the decimal by 64, round to the nearest whole number, and that's the numerator over a denominator of 64, which can then be simplified. For example, 0.311 × 64 ≈ 20, giving 20/64, which simplifies to 5/16 inch.