Decimal to Inches Calculator

Conversion direction

Decimal measurement

Type a decimal measurement. Feet-inches such as 4' 5 3/8" are accepted too.

Rounding precision

one graduation = 0.0625″ = 1.5875 mm

Inch fraction · nearest 1/16

rounded

Exact value 2.695″Fraction equals 2.6875″Error −7.5 thou · -0.1905 mm

Inch fraction: 2 11/16"
Decimal inches: 2.695"
Millimetres: 68.453 mm
Centimetres: 6.8453 cm
Metres: 0.068453 m
Feet & inches: 2 11/16"
Decimal feet: 0.22458 ft
Thou (mils): 2695 thou

Where it falls on the rule

your decimal nearest graduation rounding gap

Drag the rule or use the arrow keys — the marker moves in real time and the inch window follows. Click the tape below to jump to a different inch.

How the inch is halved down to the answer

Each row halves the row above it. The red needle is your decimal; the lit segment is the interval it lands in. The bottom row is the precision you picked, and its lit segment is the answer — see how to convert, step by step for the written method.

Convert decimal inches to fraction form, or a fraction back to a decimal, with millimetres, centimetres, metres and feet and inches alongside every result. Choose 1/8, 1/16, 1/32 or 1/64 precision and this inch fraction calculator shows the exact rounding error rather than hiding it.

Built by the DecimalToInches.com team Checked against the international inch of exactly 25.4 mm Updated 12 August 2026

On this page

01 — Definition

What Decimal to Inch Conversion Is

Decimal to inches conversion rewrites a measurement written as a decimal — 5.375 in — as whole inches plus a fraction of an inch: 5 3/8 in. The length is identical; only the notation changes.

A decimal inch comes from anything with a numeric display: calipers, micrometers, dial indicators, CAD files, spreadsheets and CNC programs all output decimals. A fractional inch comes from anything graduated: tape measures, steel rules, framing squares and architectural plans. Anyone working across both spends real time moving between the two.

The imperial system splits the inch by repeated halving rather than by tens, so inch fractions always carry denominators that are powers of two — halves, quarters, eighths, sixteenths, thirty-seconds and sixty-fourths. That is why woodworking and construction quote 3/4 in plywood and 2x4 lumber, why machining and fabrication call out 1/4 in plate and 3/8 in bar, and why crafts and hobbies — sewing, model building, leatherwork — use the same halved divisions on their rules.

It also creates the one complication worth understanding: because decimals divide by tens and inches divide by twos, the two systems do not always line up. 0.375 converts exactly to 3/8, but 0.1 has no exact inch fraction at any precision. The calculator above reports which case you are in, and by how much the rounded fraction differs from your decimal.

02 — Method

How to Convert Decimal to Inches — Step by Step

Four steps take 2.695 in to 2 11/16 in at sixteenths precision. Steps one and two are arithmetic; three and four decide the accuracy and the tidiness of the answer.

Separate the whole and decimal parts

Write the digits before the decimal point down as whole inches and set the decimal remainder aside. For 2.695 in, that is 2 whole inches with 0.695 remaining.

2.695 → W = 2, remainder 0.695

Multiply by the precision denominator

Multiply the decimal remainder by the denominator you want to round to. Sixteenths are the tape-measure standard, so multiply by 16.

0.695 × 16 = 11.12

Round to the nearest whole number

Round that product to the nearest whole number to get the numerator. 11.12 rounds down to 11. If it rounds up to the denominator itself, carry one whole inch instead.

11.12 → N = 11

Write the fraction and simplify it

Put the numerator over the denominator, then divide both by their greatest common divisor to reach lowest terms. The GCD of 11 and 16 is 1, so 11/16 is already simplified.

11/16 → 2 11/16 in

Going from inches to fraction form always involves rounding unless the decimal happens to be dyadic; going back the other way never does. So round once, straight from the original decimal to the denominator you actually want. Rounding in stages — to sixteenths and then again to eighths — compounds the error for no benefit. And watch step three: when the product rounds up to the denominator itself, the fraction closes and a whole inch carries. At sixteenths, 15.97 in gives 0.97 × 16 = 15.52, which rounds to 16, so the answer is a flat 16 in with no fractional part at all.

03 — Formula

How the Conversion Formula Works

Five variables carry a decimal to a simplified inch fraction. Each is defined below, then applied to a worked conversion.

N=round ( D_f × P ) , R=W+ N ÷ CP ÷ C

D_f is the decimal's fractional part and W its whole part. C is the greatest common divisor of N and P, which reduces the fraction to lowest terms. If N reaches P, add one to W and reset N to zero.

D The input decimal — the measurement in decimal inches, such as 2.695.
P The precision denominator you round to: 8, 16, 32 or 64. Always a power of two.
N The numerator — the decimal part multiplied by P, rounded to the nearest whole number.
C The greatest common divisor of N and P, used to simplify the fraction.
R The final result — whole inches plus the simplified inch fraction.

Worked calculation — D = 2.695, P = 16

W = 2, D_f = 0.695 Separate whole inches from the decimal part
0.695 × 16 = 11.12 Multiply the decimal part by the precision
N = 11 Round 11.12 to the nearest whole number
C = GCD(11, 16) = 1 Already in lowest terms

R = 2 11/16″ = 2.6875″ (−7.5 thou)

The formula returns an approximation, not an equality, whenever D_f × P fails to land on a whole number. The gap between the rounded fraction and the original decimal is the rounding error, and it can never exceed half a graduation — 1/(2P) — in either direction. Here 2 11/16 in is 2.6875 in, seven and a half thousandths short of 2.695 in.

That ceiling is the measurement tolerance your chosen value of P carries, and it is fixed rather than a matter of judgement: rounding to the nearest 1/16 can leave 1/32 in on the table, the nearest 1/32 halves that again, and the nearest 1/64 halves it once more. The table below sets it out for every precision the calculator offers.

One caution, because it is the most common misuse: P sets the measurement precision of the answer and nothing else. Raising it improves measurement resolution without improving accuracy — asking for sixty-fourths of a value read off a tape marked in sixteenths invents detail the tool never captured. Match P to the instrument that took the measurement.

One graduation at each precision, and the worst-case rounding error — always half a graduation — that P introduces.
Precision (P)	One graduation	In mm	Worst-case error	Typical use
1/2″	0.5″	12.7 mm	±0.25″ · ±6.35 mm	Rough demolition and site layout.
1/4″	0.25″	6.35 mm	±0.125″ · ±3.175 mm	Concrete forms, landscaping, rough carpentry.
1/8″	0.125″	3.175 mm	±0.0625″ · ±1.5875 mm	General construction and framing.
1/16″	0.0625″	1.5875 mm	±0.03125″ · ±0.79375 mm	Standard tape-measure work: trim, joinery, most woodworking.
1/32″	0.03125″	0.79375 mm	±0.015625″ · ±0.396875 mm	Cabinetmaking, sheet metal, fine joinery.
1/64″	0.015625″	0.396875 mm	±0.0078125″ · ±0.198437 mm	Machining, toolmaking, engineering drawings.
1/128″	0.0078125″	0.198437 mm	±0.00390625″ · ±0.099219 mm	Precision grinding and inspection; rarely marked on a rule.

Metric output needs no extra rounding step: multiply the decimal by 25.4 for millimetres or 2.54 for centimetres, both exact by definition since the international yard and pound agreement of 1959. The calculator returns millimetres, centimetres and metres alongside the fraction, so a mixed-unit drawing takes one pass. Going the other way is where the rounding reappears — a metric value almost never has an exact inch fraction, and 100 mm works out to 3.937008 in, or 3 15/16 in at sixty-fourths.

04 — Reference chart

Inch Fraction Chart to 1/64

All 64 graduations of an inch, from 1/64 in to 1 in, with each fraction reduced to lowest terms. Every decimal and millimetre value is exact, not rounded — sixty-fourths of an inch terminate at six decimal places in both units. Use this decimal to inches chart as a lookup when you would rather not run the arithmetic, and filter it to the precision you are working to.

Show

Inch fraction to decimal inch and millimetre. Coarser graduations are set in bold, so the 1/4 and 1/8 marks stay findable inside 64 rows.
Fraction	Decimal (in)	Millimetres
1/64″	0.015625	0.396875
1/32″	0.03125	0.79375
3/64″	0.046875	1.190625
1/16″	0.0625	1.5875
5/64″	0.078125	1.984375
3/32″	0.09375	2.38125
7/64″	0.109375	2.778125
1/8″	0.125	3.175
9/64″	0.140625	3.571875
5/32″	0.15625	3.96875
11/64″	0.171875	4.365625
3/16″	0.1875	4.7625
13/64″	0.203125	5.159375
7/32″	0.21875	5.55625
15/64″	0.234375	5.953125
1/4″	0.25	6.35
17/64″	0.265625	6.746875
9/32″	0.28125	7.14375
19/64″	0.296875	7.540625
5/16″	0.3125	7.9375
21/64″	0.328125	8.334375
11/32″	0.34375	8.73125
23/64″	0.359375	9.128125
3/8″	0.375	9.525
25/64″	0.390625	9.921875
13/32″	0.40625	10.31875
27/64″	0.421875	10.715625
7/16″	0.4375	11.1125
29/64″	0.453125	11.509375
15/32″	0.46875	11.90625
31/64″	0.484375	12.303125
1/2″	0.5	12.7
33/64″	0.515625	13.096875
17/32″	0.53125	13.49375
35/64″	0.546875	13.890625
9/16″	0.5625	14.2875
37/64″	0.578125	14.684375
19/32″	0.59375	15.08125
39/64″	0.609375	15.478125
5/8″	0.625	15.875
41/64″	0.640625	16.271875
21/32″	0.65625	16.66875
43/64″	0.671875	17.065625
11/16″	0.6875	17.4625
45/64″	0.703125	17.859375
23/32″	0.71875	18.25625
47/64″	0.734375	18.653125
3/4″	0.75	19.05
49/64″	0.765625	19.446875
25/32″	0.78125	19.84375
51/64″	0.796875	20.240625
13/16″	0.8125	20.6375
53/64″	0.828125	21.034375
27/32″	0.84375	21.43125
55/64″	0.859375	21.828125
7/8″	0.875	22.225
57/64″	0.890625	22.621875
29/32″	0.90625	23.01875
59/64″	0.921875	23.415625
15/16″	0.9375	23.8125
61/64″	0.953125	24.209375
31/32″	0.96875	24.60625
63/64″	0.984375	25.003125
1″	1	25.4

05 — Reverse direction

How to Convert Inch Fractions to Decimal

Divide the numerator by the denominator and add the whole inches. For 5 3/8 in, 3 ÷ 8 = 0.375, so the decimal is 5.375 in.

This direction is the simpler of the two, because no rounding is involved — it is exact rather than approximate. Every inch fraction has an exact decimal form — the denominator is always a power of two, and any fraction with a power-of-two denominator terminates as a decimal rather than repeating. 1/16 is exactly 0.0625, 1/32 is exactly 0.03125, and 1/64 is exactly 0.015625. Nothing is lost, so no precision setting applies.

For a mixed number, convert the fractional part and add it to the whole: 2 11/16 in becomes 11 ÷ 16 = 0.6875, then 2 + 0.6875 = 2.6875 in. If the fraction is not in lowest terms the answer is the same either way — 6/16 and 3/8 both divide out to 0.375.

Set the calculator at the top of this page to Fraction → Decimal and it runs this direction, accepting 5 3/8, 5-3/8 or a bare 3/8, and returning the decimal alongside millimetres, centimetres and feet.

06 — Feet

Decimal Feet to Inches

Multiply the decimal part of a feet value by 12 to get inches, and keep the whole number as feet. 4.45 ft is 4 ft plus 0.45 × 12 = 5.4 in, which at sixteenths is 4 ft 5 3/8 in.

A decimal foot is not the same animal as a decimal inch, and confusing them is a costly mistake: 4.5 ft is four and a half feet, or 54 in, while 4.5 in is four and a half inches. Surveying, civil engineering and site drawings routinely use decimal feet; carpentry uses feet with fractional inches. To go the other way, divide the inches by 12 and add the whole feet — 4 ft 5 3/8 in is 5.375 ÷ 12 = 0.4479, so 4.4479 ft.

Decimal feet from 0.1 to 1.0, with the equivalent in decimal inches, the nearest sixteenth, and millimetres.
Decimal feet	Inches (decimal)	Nearest 1/16	Millimetres
0.1 ft	1.2″	1 3/16″	30.48 mm
0.2 ft	2.4″	2 3/8″	60.96 mm
0.3 ft	3.6″	3 5/8″	91.44 mm
0.4 ft	4.8″	4 13/16″	121.92 mm
0.5 ft	6″	6″	152.4 mm
0.6 ft	7.2″	7 3/16″	182.88 mm
0.7 ft	8.4″	8 3/8″	213.36 mm
0.8 ft	9.6″	9 5/8″	243.84 mm
0.9 ft	10.8″	10 13/16″	274.32 mm
1 ft	12″	12″	304.8 mm

07 — Reading the tool

How to Read Decimal Inches on a Tape Measure

A tape measure encodes the fraction in the height of each mark, not in any number. Convert your decimal to a fraction first, then find that fraction by tick height rather than by counting every graduation.

Step one

Find the tallest

Between two numbered inch marks, the single tallest line is the half inch. It splits the inch in two and is your first landmark — everything else is read relative to it.

Step two

Work down the heights

The next tallest pair are the quarters, then the eighths, and the shortest marks are the sixteenths. Tick height always tells you the denominator, which is why you never have to count sixteen marks.

Step three

Count and simplify

Count the shortest marks from the last inch number, put that count over 16 and reduce. Four sixteenths past 7 in is 7 4/16 in, which simplifies to 7 1/4 in.

Most tape measures stop at 1/16 in; better tapes mark 1/32 for the first few inches only, and machinist steel rules go to 1/64. Below that, graduations stop being useful and measurement moves to instruments that read decimals directly — a vernier caliper resolves to 0.001 in, a digital caliper displays it outright, and a micrometer reaches 0.0001 in. If your value needs finer resolution than 1/64, that is the signal to stay in decimal inches rather than convert.

One practical note: the hook at the end of a tape measure is deliberately loose by about 1/16 in, so it reads correctly whether you pull against it or push up to it. That is not a defect and needs no correction in the arithmetic.

08 — Applications

Why Fractional Inches Matter

Fractions are not a legacy quirk in these trades — they are the working notation, and the material itself is sold and specified in them.

Every denominator on a rule — 2, 4, 8, 16, 32, 64 — is a power of two, because bisection is the one subdivision that needs no measurement. Fold a length in half for halves, again for quarters, again for eighths; a rule-maker could graduate a scale with dividers alone. Mathematicians call these dyadic fractions, or dyadic rational numbers, and any dyadic fraction terminates as a decimal — which is why every value in the chart above is exact rather than rounded. It also explains what fails: 0.1 in needs a factor of five in its denominator, and no amount of halving produces a five.

1/16″ · sometimes 1/32″

Woodworking & construction

Lumber and sheet goods are specified in fractions: 3/4 in plywood, 1/2 in drywall, 5/4 decking. A 2x4 actually measures 1 1/2 by 3 1/2 in after surfacing, so every framing calculation runs in fractions from the start.

Tape measures are graduated to 1/16 in, which is why cut lists are written to that precision. Trim and finish carpentry hold the same sixteenths, tightening to thirty-seconds where two mitres have to close without a visible gap.

1/64″ · thousandths

Machining & fabrication

Stock and tooling are named in fractions — 1/4 in plate, 3/8 in bar, a 1/4 in drill bit, a 3/8 in wrench — but every tolerance and machine coordinate is decimal, to three or four places. SAE fasteners follow the same convention, sized in inch fractions where metric fasteners are sized in millimetres. Fractions name the material; decimals control the cut.

That split is exactly why this conversion matters in a shop: a drawing may call out 3/8 in stock while the CNC program needs 0.375 in, and a caliper reading of 0.3752 in has to be judged against a fractional nominal size.

1/8″ · 1/16″

Crafts & hobbies

Sewing patterns specify seam allowances in fractions — 5/8 in is the garment standard, 1/4 in for quilting — and quilting rules are printed in eighths and sixteenths for exactly that reason.

Model building, leatherwork and jewellery making follow the same convention, with scale rules and stock thicknesses quoted in fractions. A 1/8 in dowel or a 1/16 in sheet is ordered by its fraction, not its decimal.

09 — Decimal equivalents

Decimal Equivalent Chart — Drill & Stock Sizes

Fractional drill bits and stock sizes with their decimal and millimetre equivalents. These are the fractions you will actually meet on a drawing or an index, and the decimals a caliper will read back to you.

Common fractional drill and stock sizes. Clearance sizes follow the usual shop rule of one sixteenth over the nominal bolt diameter.
Fraction	Decimal (in)	Millimetres	Common use
1/16″	0.0625	1.5875	Pilot holes for small wood screws
3/32″	0.09375	2.3812	Pilot holes in hardwood for #6 screws
1/8″	0.125	3.175	General-purpose pilot and anchor holes
5/32″	0.15625	3.9688	Pilot holes for #10 screws in softwood
3/16″	0.1875	4.7625	Clearance holes for #10 screws; small anchors
7/32″	0.21875	5.5562	Clearance for 3/16 in bolts
1/4″	0.25	6.35	1/4 in dowels, bolts and masonry anchors
9/32″	0.28125	7.1437	Undersized clearance for 1/4 in bolts
5/16″	0.3125	7.9375	Standard clearance for 1/4 in bolts
3/8″	0.375	9.525	3/8 in dowels and bolts; common wrench size
7/16″	0.4375	11.1125	Standard clearance for 3/8 in bolts
1/2″	0.5	12.7	1/2 in dowels, conduit and bolts
9/16″	0.5625	14.2875	Standard clearance for 1/2 in bolts
5/8″	0.625	15.875	5/8 in bolts and larger dowel stock
11/16″	0.6875	17.4625	Standard clearance for 5/8 in bolts
3/4″	0.75	19.05	3/4 in dowels; spade and Forstner bit sizing
7/8″	0.875	22.225	Large clearance holes and hole-saw pilots
1″	1	25.4	Hole saws, Forstner bits, 1 in stock

10 — Quick reference

Popular Conversions Quick Reference

The sixteen sixteenth-inch steps, each with its simplified fraction and exact millimetre value. These cover most of the decimal values that turn up on a drawing or a caliper.

0.0625″: 1/16″ 1.5875 mm
0.125″: 1/8″ 3.175 mm
0.1875″: 3/16″ 4.7625 mm
0.25″: 1/4″ 6.35 mm
0.3125″: 5/16″ 7.9375 mm
0.375″: 3/8″ 9.525 mm
0.4375″: 7/16″ 11.1125 mm
0.5″: 1/2″ 12.7 mm
0.5625″: 9/16″ 14.2875 mm
0.625″: 5/8″ 15.875 mm
0.6875″: 11/16″ 17.4625 mm
0.75″: 3/4″ 19.05 mm
0.8125″: 13/16″ 20.6375 mm
0.875″: 7/8″ 22.225 mm
0.9375″: 15/16″ 23.8125 mm
1″: 1″ 25.4 mm

11 — Questions

Frequently Asked Questions

What is a decimal inch?

A decimal inch is an inch measurement written with a decimal fraction — 5.375 in — instead of a common fraction such as 5 3/8 in. Both describe the same length; only the notation differs. Decimal inches come off calipers, micrometers, dial indicators, CAD files and CNC programs, while fractional inches are what a tape measure, steel rule or architectural drawing gives you. Because a decimal inch can hold any value, it can also express lengths that no ruler graduation matches exactly.

How do you convert decimal to inches?

Multiply the decimal part by your chosen precision denominator, round the result to the nearest whole number, and write that number over the denominator. Keep the digits before the decimal point as whole inches, then reduce the fraction by its greatest common divisor. For 5.375 in at 1/16 precision: 0.375 × 16 = 6, giving 6/16, which reduces to 3/8 — so the answer is 5 3/8 in.

What is 0.625 inches as a fraction?

0.625 inches is exactly 5/8 of an inch. Multiplying 0.625 by 8 gives exactly 5 with no remainder, so no rounding is involved and the conversion is exact. In metric it is 15.875 mm, and it is the decimal stamped on 5/8 in bolts, plywood and drill bits.

What does rounding precision mean?

Rounding precision is the denominator you round the fraction to — 1/8, 1/16, 1/32 or 1/64 — and it sets the finest graduation the answer can land on. A higher denominator gives a closer answer: rounding to the nearest 1/16 can be off by as much as half a graduation, or 1/32 in, while rounding to 1/64 narrows that worst case to 1/128 in. Choose the precision that matches the tool doing the measuring, not the largest number available.

How do you read decimal inches on a ruler?

You cannot read a decimal directly on a fractional ruler — convert it to the nearest inch fraction first, then count graduations. Find the whole inch, then count the shortest marks past it: on a standard tape those are sixteenths, so four of them past the 7 in mark is 7 4/16 in, which reduces to 7 1/4 in. The ruler in the calculator above shows exactly where a decimal falls between two graduations, including when it lands between them.

What is an inch fraction?

An inch fraction is a fraction of an inch whose denominator is a power of two — 1/2, 1/4, 1/8, 1/16, 1/32 or 1/64. Mathematicians call these dyadic fractions, and they exist because a rule is graduated by repeatedly halving the inch rather than by dividing it into tenths. That is also why fractions such as 1/3 or 1/10 appear on no ruler: their denominators are not powers of two.

How big is one inch in mm and cm?

One inch is exactly 25.4 millimetres, which is 2.54 centimetres or 0.0254 metres. That figure is a definition rather than a measurement — it was fixed by the international yard and pound agreement of 1959 — so converting between inches and millimetres loses no precision in either direction. Multiply inches by 25.4 for millimetres, or divide millimetres by 25.4 for inches.

Why does the US use inches instead of the metric system?

The United States inherited its units from the British imperial system and never made the switch compulsory. The Metric Act of 1866 made metric units legal for trade, and the Metric Conversion Act of 1975 declared metric the preferred system, but both left adoption voluntary. With an enormous installed base of imperial tooling, fasteners, lumber dimensions and building codes, the cost of converting has kept inches in everyday use for construction and consumer goods, even though US science, medicine and much of manufacturing already work in metric.

What is the symbol for inches?

The symbol for inches is the double prime, ″, though in practice it is almost always typed as a straight double quote — 5.375". Feet use the single prime, ′, typed as an apostrophe, so 4 ft 5 in is written 4' 5". The abbreviation "in" is the formal SI-style symbol and is preferred in engineering documentation where a quote mark could be misread.

How do you convert decimal feet to inches?

Multiply the decimal part of the feet value by 12, then keep the whole number as feet. For 4.45 ft: 0.45 × 12 = 5.4, so the measurement is 4 ft 5.4 in, and 5.4 in rounds to 5 3/8 in at sixteenths. Surveying and civil drawings routinely use decimal feet while carpentry uses feet with fractional inches, so this conversion comes up whenever the two trades share a drawing.