Fraction to Decimal Conversion Chart for Wrenches & Sockets
Fraction to Decimal Calculator
- Decimal inches
- 0.8750"
- numerator ÷ denominator
- Millimetres
- 22.225mm
- in × 25.4
- Sixty-fourths
- 56/64
- common denominator
7/8" equals 0.8750 inches, which is 22.225mm, or 56/64" expressed over the common denominator.
Quick sizes
Accepts a simple fraction (7/8), a mixed number (1-1/4), or a decimal. The sixty-fourths card restates the value over the common denominator used across every SAE tool range.
To convert a fraction to a decimal, divide the numerator by the denominator: 7/8 becomes 7 ÷ 8 = 0.875 inches. Every fraction used on a wrench or socket is a power of two, halves down through sixty-fourths, so all of them produce short, exact decimals with no repeating digits. That is the entire method, and it is worth knowing because the decimal is the only form in which two sizes can be honestly compared. Nobody can tell at a glance whether 19/32" is larger than 5/8", but 0.594" against 0.625" answers it instantly. Getting to the decimal is also the first step in every metric conversion, which is why the socket conversion calculator runs it internally before matching a size.
Most Common Wrench and Socket Fractions
The sizes that actually appear in a combination wrench set or socket rail, rather than every mathematically possible 64th.
| Fraction | Decimal inches | Millimetres |
|---|---|---|
| 1/8" | 0.1250 | 3.17mm |
| 5/32" | 0.1563 | 3.97mm |
| 3/16" | 0.1875 | 4.76mm |
| 7/32" | 0.2188 | 5.56mm |
| 1/4" | 0.2500 | 6.35mm |
| 9/32" | 0.2813 | 7.14mm |
| 5/16" | 0.3125 | 7.94mm |
| 11/32" | 0.3438 | 8.73mm |
| 3/8" | 0.3750 | 9.52mm |
| 13/32" | 0.4063 | 10.32mm |
| 7/16" | 0.4375 | 11.11mm |
| 15/32" | 0.4688 | 11.91mm |
| 1/2" | 0.5000 | 12.70mm |
| 17/32" | 0.5313 | 13.49mm |
| 9/16" | 0.5625 | 14.29mm |
| 19/32" | 0.5938 | 15.08mm |
| 5/8" | 0.6250 | 15.88mm |
| 21/32" | 0.6563 | 16.67mm |
| 11/16" | 0.6875 | 17.46mm |
| 23/32" | 0.7188 | 18.26mm |
| 3/4" | 0.7500 | 19.05mm |
| 13/16" | 0.8125 | 20.64mm |
| 7/8" | 0.8750 | 22.22mm |
| 29/32" | 0.9063 | 23.02mm |
| 15/16" | 0.9375 | 23.81mm |
| 1" | 1.0000 | 25.40mm |
| 1-1/8" | 1.1250 | 28.57mm |
| 1-1/4" | 1.2500 | 31.75mm |
| 1-3/8" | 1.3750 | 34.92mm |
| 1-1/2" | 1.5000 | 38.10mm |
| 1-5/8" | 1.6250 | 41.27mm |
| 1-3/4" | 1.7500 | 44.45mm |
| 1-7/8" | 1.8750 | 47.63mm |
| 2" | 2.0000 | 50.80mm |
This shorter list is the one worth committing to memory. The steps are uneven by design: the range climbs in 32nds through the small sizes where precision matters most, widens to 16ths through the middle of the set, and opens to 8ths at the top where the fasteners are large enough that the proportional error stays small. The millimetre column is the exact conversion, not the nearest socket. For that, the SAE to metric chart adds the matching step.
Worked Example: 7/8 as a Decimal
Step 1: Divide
7 ÷ 8 = 0.875
The numerator divided by the denominator. Because 8 is a power of two the division terminates after three decimal places.
Step 2: Over 64ths
0.875 × 64 = 56/64
Restating over the common denominator makes 7/8" directly comparable with 55/64" or 57/64", which is how machinists rank adjacent sizes.
Step 3: To metric
0.875 × 25.4 = 22.23mm
Multiplying the decimal by 25.4 gives the exact millimetre value. The nearest socket is 22mm, 0.23mm undersize.
Those three steps are the whole workflow, and they compose in either direction. Running them backwards, millimetres to decimal to fraction, is what the millimetre to inches chart does, and applying the result to hex keys instead of sockets is covered on the Allen wrench size chart, where the tolerances are tighter still.
Full Fraction Chart: 1/64" to 2"
All 128 sixty-fourths, each with its reduced fraction, decimal inch value, and millimetre equivalent.
| Fraction | Sixty-fourths | Decimal inches | Millimetres |
|---|---|---|---|
| 1/64" | 1/64 | 0.0156 | 0.40mm |
| 1/32" | 2/64 | 0.0313 | 0.79mm |
| 3/64" | 3/64 | 0.0469 | 1.19mm |
| 1/16" | 4/64 | 0.0625 | 1.59mm |
| 5/64" | 5/64 | 0.0781 | 1.98mm |
| 3/32" | 6/64 | 0.0938 | 2.38mm |
| 7/64" | 7/64 | 0.1094 | 2.78mm |
| 1/8" | 8/64 | 0.1250 | 3.17mm |
| 9/64" | 9/64 | 0.1406 | 3.57mm |
| 5/32" | 10/64 | 0.1563 | 3.97mm |
| 11/64" | 11/64 | 0.1719 | 4.37mm |
| 3/16" | 12/64 | 0.1875 | 4.76mm |
| 13/64" | 13/64 | 0.2031 | 5.16mm |
| 7/32" | 14/64 | 0.2188 | 5.56mm |
| 15/64" | 15/64 | 0.2344 | 5.95mm |
| 1/4" | 16/64 | 0.2500 | 6.35mm |
| 17/64" | 17/64 | 0.2656 | 6.75mm |
| 9/32" | 18/64 | 0.2813 | 7.14mm |
| 19/64" | 19/64 | 0.2969 | 7.54mm |
| 5/16" | 20/64 | 0.3125 | 7.94mm |
| 21/64" | 21/64 | 0.3281 | 8.33mm |
| 11/32" | 22/64 | 0.3438 | 8.73mm |
| 23/64" | 23/64 | 0.3594 | 9.13mm |
| 3/8" | 24/64 | 0.3750 | 9.52mm |
| 25/64" | 25/64 | 0.3906 | 9.92mm |
| 13/32" | 26/64 | 0.4063 | 10.32mm |
| 27/64" | 27/64 | 0.4219 | 10.72mm |
| 7/16" | 28/64 | 0.4375 | 11.11mm |
| 29/64" | 29/64 | 0.4531 | 11.51mm |
| 15/32" | 30/64 | 0.4688 | 11.91mm |
| 31/64" | 31/64 | 0.4844 | 12.30mm |
| 1/2" | 32/64 | 0.5000 | 12.70mm |
| 33/64" | 33/64 | 0.5156 | 13.10mm |
| 17/32" | 34/64 | 0.5313 | 13.49mm |
| 35/64" | 35/64 | 0.5469 | 13.89mm |
| 9/16" | 36/64 | 0.5625 | 14.29mm |
| 37/64" | 37/64 | 0.5781 | 14.68mm |
| 19/32" | 38/64 | 0.5938 | 15.08mm |
| 39/64" | 39/64 | 0.6094 | 15.48mm |
| 5/8" | 40/64 | 0.6250 | 15.88mm |
| 41/64" | 41/64 | 0.6406 | 16.27mm |
| 21/32" | 42/64 | 0.6563 | 16.67mm |
| 43/64" | 43/64 | 0.6719 | 17.07mm |
| 11/16" | 44/64 | 0.6875 | 17.46mm |
| 45/64" | 45/64 | 0.7031 | 17.86mm |
| 23/32" | 46/64 | 0.7188 | 18.26mm |
| 47/64" | 47/64 | 0.7344 | 18.65mm |
| 3/4" | 48/64 | 0.7500 | 19.05mm |
| 49/64" | 49/64 | 0.7656 | 19.45mm |
| 25/32" | 50/64 | 0.7813 | 19.84mm |
| 51/64" | 51/64 | 0.7969 | 20.24mm |
| 13/16" | 52/64 | 0.8125 | 20.64mm |
| 53/64" | 53/64 | 0.8281 | 21.03mm |
| 27/32" | 54/64 | 0.8438 | 21.43mm |
| 55/64" | 55/64 | 0.8594 | 21.83mm |
| 7/8" | 56/64 | 0.8750 | 22.22mm |
| 57/64" | 57/64 | 0.8906 | 22.62mm |
| 29/32" | 58/64 | 0.9063 | 23.02mm |
| 59/64" | 59/64 | 0.9219 | 23.42mm |
| 15/16" | 60/64 | 0.9375 | 23.81mm |
| 61/64" | 61/64 | 0.9531 | 24.21mm |
| 31/32" | 62/64 | 0.9688 | 24.61mm |
| 63/64" | 63/64 | 0.9844 | 25.00mm |
| 1" | 64/64 | 1.0000 | 25.40mm |
| 1-1/64" | 65/64 | 1.0156 | 25.80mm |
| 1-1/32" | 66/64 | 1.0313 | 26.19mm |
| 1-3/64" | 67/64 | 1.0469 | 26.59mm |
| 1-1/16" | 68/64 | 1.0625 | 26.99mm |
| 1-5/64" | 69/64 | 1.0781 | 27.38mm |
| 1-3/32" | 70/64 | 1.0938 | 27.78mm |
| 1-7/64" | 71/64 | 1.1094 | 28.18mm |
| 1-1/8" | 72/64 | 1.1250 | 28.57mm |
| 1-9/64" | 73/64 | 1.1406 | 28.97mm |
| 1-5/32" | 74/64 | 1.1563 | 29.37mm |
| 1-11/64" | 75/64 | 1.1719 | 29.77mm |
| 1-3/16" | 76/64 | 1.1875 | 30.16mm |
| 1-13/64" | 77/64 | 1.2031 | 30.56mm |
| 1-7/32" | 78/64 | 1.2188 | 30.96mm |
| 1-15/64" | 79/64 | 1.2344 | 31.35mm |
| 1-1/4" | 80/64 | 1.2500 | 31.75mm |
| 1-17/64" | 81/64 | 1.2656 | 32.15mm |
| 1-9/32" | 82/64 | 1.2813 | 32.54mm |
| 1-19/64" | 83/64 | 1.2969 | 32.94mm |
| 1-5/16" | 84/64 | 1.3125 | 33.34mm |
| 1-21/64" | 85/64 | 1.3281 | 33.73mm |
| 1-11/32" | 86/64 | 1.3438 | 34.13mm |
| 1-23/64" | 87/64 | 1.3594 | 34.53mm |
| 1-3/8" | 88/64 | 1.3750 | 34.92mm |
| 1-25/64" | 89/64 | 1.3906 | 35.32mm |
| 1-13/32" | 90/64 | 1.4063 | 35.72mm |
| 1-27/64" | 91/64 | 1.4219 | 36.12mm |
| 1-7/16" | 92/64 | 1.4375 | 36.51mm |
| 1-29/64" | 93/64 | 1.4531 | 36.91mm |
| 1-15/32" | 94/64 | 1.4688 | 37.31mm |
| 1-31/64" | 95/64 | 1.4844 | 37.70mm |
| 1-1/2" | 96/64 | 1.5000 | 38.10mm |
| 1-33/64" | 97/64 | 1.5156 | 38.50mm |
| 1-17/32" | 98/64 | 1.5313 | 38.89mm |
| 1-35/64" | 99/64 | 1.5469 | 39.29mm |
| 1-9/16" | 100/64 | 1.5625 | 39.69mm |
| 1-37/64" | 101/64 | 1.5781 | 40.08mm |
| 1-19/32" | 102/64 | 1.5938 | 40.48mm |
| 1-39/64" | 103/64 | 1.6094 | 40.88mm |
| 1-5/8" | 104/64 | 1.6250 | 41.27mm |
| 1-41/64" | 105/64 | 1.6406 | 41.67mm |
| 1-21/32" | 106/64 | 1.6563 | 42.07mm |
| 1-43/64" | 107/64 | 1.6719 | 42.47mm |
| 1-11/16" | 108/64 | 1.6875 | 42.86mm |
| 1-45/64" | 109/64 | 1.7031 | 43.26mm |
| 1-23/32" | 110/64 | 1.7188 | 43.66mm |
| 1-47/64" | 111/64 | 1.7344 | 44.05mm |
| 1-3/4" | 112/64 | 1.7500 | 44.45mm |
| 1-49/64" | 113/64 | 1.7656 | 44.85mm |
| 1-25/32" | 114/64 | 1.7813 | 45.24mm |
| 1-51/64" | 115/64 | 1.7969 | 45.64mm |
| 1-13/16" | 116/64 | 1.8125 | 46.04mm |
| 1-53/64" | 117/64 | 1.8281 | 46.43mm |
| 1-27/32" | 118/64 | 1.8438 | 46.83mm |
| 1-55/64" | 119/64 | 1.8594 | 47.23mm |
| 1-7/8" | 120/64 | 1.8750 | 47.63mm |
| 1-57/64" | 121/64 | 1.8906 | 48.02mm |
| 1-29/32" | 122/64 | 1.9063 | 48.42mm |
| 1-59/64" | 123/64 | 1.9219 | 48.82mm |
| 1-15/16" | 124/64 | 1.9375 | 49.21mm |
| 1-61/64" | 125/64 | 1.9531 | 49.61mm |
| 1-31/32" | 126/64 | 1.9688 | 50.01mm |
| 1-63/64" | 127/64 | 1.9844 | 50.40mm |
| 2" | 128/64 | 2.0000 | 50.80mm |
The Fraction column shows each value reduced to lowest terms while the Sixty-fourths column keeps the common denominator, so the same row reads both ways: 32/64 and 1/2 are the same size, and seeing them side by side is what makes the ranking obvious. The millimetre column is the exact equivalent, useful for machining, but note that almost none of these values coincide with a real metric tool size.
Reading Fractional Sizes on a Socket Set
SAE sets are laid out in fraction order, which is not the same as numeric order to the untrained eye. A typical 3/8" drive rail runs 1/4, 5/16, 11/32, 3/8, 7/16, 1/2, 9/16, 5/8, 11/16, 3/4, denominators jumping between 4, 8, 16 and 32 as the steps change size. The reliable way to read a rail is to convert mentally to 64ths, where that same run becomes 16, 20, 22, 24, 28, 32, 36, 40, 44, 48 and the ordering is plain. Sockets stamped with a bare fraction are SAE; sockets stamped with a plain whole number are metric. A socket stamped 13 is 13mm, and a socket stamped 1/2 is 0.5", and those two are the classic confusable pair, 0.512" against 0.500". Checking whether that 0.012" gap is survivable on a given fastener is exactly what the two-way socket conversion calculator is for.
Frequently Asked Questions
Common questions about fractional tool sizes and their decimal equivalents.
How do you convert a fraction to a decimal?
Divide the numerator by the denominator. 7/8 becomes 7 ÷ 8 = 0.875. For a mixed number, convert the fractional part and add the whole number: 1-1/4" is 1 + (1 ÷ 4) = 1.25". Every wrench fraction reduces to a clean decimal because all of them are powers of two, halves, quarters, eighths, sixteenths, thirty-seconds and sixty-fourths, so none of them produce a repeating decimal.
What is 7/8 as a decimal?
7/8 is 0.875 inches, or 22.23mm. It is one of the most common wrench and socket sizes, used on oxygen sensors and larger suspension hardware, and its closest metric partner is 22mm at 0.866", a difference of 0.009", which puts the pair in the Use with Caution band rather than a free swap.
Why are socket sizes given in 64ths?
Because 64 is the smallest common denominator that expresses every step in the SAE range as a whole number. 1/2" is 32/64, 9/16" is 36/64, 19/32" is 38/64. Putting everything over the same denominator is what lets you compare two fractions at a glance, 19/32" and 5/8" are hard to rank by eye, but 38/64 and 40/64 are not.
What is the difference between 9/16 and 5/8?
9/16" is 0.5625" and 5/8" is 0.625", a difference of 0.0625" or exactly one sixteenth of an inch. In millimetres that is 14.29mm against 15.88mm, a gap of 1.59mm, which is more than a full socket step. They are adjacent sizes in a set, and mistaking one for the other is a common cause of a rounded head because 9/16" will not seat on a 5/8" fastener at all.
How do I read the fraction stamped on a socket?
The number stamped on the side is the opening measured across the flats, in inches. A bare fraction such as 21/32 means SAE; a plain whole number such as 17 means 17mm. Some sockets carry both. If the stamping has worn away, measure the opening across two opposing flats with a caliper and match the decimal against the chart on this page.
More Conversion Tools
The rest of the fastener, thread and drill references on this site, every one of them is one click away from here.