Calculator inputs and options
Enter one value for a detailed result, or paste many values for a batch conversion table.
Sixteenth fraction reference table
Every step equals 0.0625. Simplified fractions are shown beside their fixed-denominator forms.
| Sixteenth | Simplified | Decimal | Percentage | Common ruler name |
|---|---|---|---|---|
| 0/16 | 0 | 0 | 0% | Zero |
| 1/16 | 1/16 | 0.0625 | 6.25% | 1 sixteenths |
| 2/16 | 1/8 | 0.125 | 12.5% | One eighth |
| 3/16 | 3/16 | 0.1875 | 18.75% | 3 sixteenths |
| 4/16 | 1/4 | 0.25 | 25% | One quarter |
| 5/16 | 5/16 | 0.3125 | 31.25% | 5 sixteenths |
| 6/16 | 3/8 | 0.375 | 37.5% | Three eighths |
| 7/16 | 7/16 | 0.4375 | 43.75% | 7 sixteenths |
| 8/16 | 1/2 | 0.5 | 50% | One half |
| 9/16 | 9/16 | 0.5625 | 56.25% | 9 sixteenths |
| 10/16 | 5/8 | 0.625 | 62.5% | Five eighths |
| 11/16 | 11/16 | 0.6875 | 68.75% | 11 sixteenths |
| 12/16 | 3/4 | 0.75 | 75% | Three quarters |
| 13/16 | 13/16 | 0.8125 | 81.25% | 13 sixteenths |
| 14/16 | 7/8 | 0.875 | 87.5% | Seven eighths |
| 15/16 | 15/16 | 0.9375 | 93.75% | 15 sixteenths |
| 16/16 | 1 | 1 | 100% | One whole |
Formula used
For a decimal value x, multiply by 16, apply the selected rounding rule, then place the resulting integer over 16.
n = round(x × 16) sixteenth fraction = n / 16For a mixed number, divide the absolute numerator by 16. The quotient is the whole number, and the remainder is the sixteenth numerator.
whole = floor(|n| ÷ 16), remainder = |n| mod 16The fraction is simplified by dividing its numerator and denominator by their greatest common divisor.
simplified fraction = (n ÷ gcd(n,16)) / (16 ÷ gcd(n,16))Worked example: 2.6875
- Multiply the decimal by 16: 2.6875 × 16 = 43.
- Place the integer over 16: 43/16.
- Separate the whole number: 43 ÷ 16 gives 2 with remainder 11.
- The mixed-number answer is 2 11/16.
How to use this calculator
- Type a positive or negative decimal in the main input field.
- Choose ordinary decimal mode or decimal-feet measurement mode.
- Select the rounding rule required by your project or standard.
- Choose a mixed, improper, fixed-denominator, or Unicode display.
- Add a measurement unit and enter an acceptable error tolerance.
- Press “Convert decimal” to view the fraction, nearby values, and error analysis.
- For many values, paste a list into the batch field and press “Convert batch.”
- Copy, print, share, or export the resulting measurements as needed.
Understanding decimal-to-sixteenth conversion
A sixteenth fraction divides one whole unit into sixteen equal parts. Each step is exactly 0.0625, so common ruler marks such as 1/4, 1/2, and 3/4 are also members of the sixteenth system. For example, 4/16 simplifies to 1/4, 8/16 simplifies to 1/2, and 12/16 simplifies to 3/4. Keeping the denominator at 16 is useful when comparing positions on a ruler because every result shares the same scale.
The calculator first multiplies the decimal by sixteen. A decimal of 0.375 becomes 6 after multiplication, producing 6/16. Reducing both numbers by their greatest common divisor changes 6/16 to 3/8. When the decimal is larger than one, the same method creates an improper fraction. The calculator then separates complete groups of sixteen to display a mixed number. Thus, 2.6875 becomes 43/16 and then 2 11/16.
Not every decimal lands exactly on a sixteenth. A value such as 0.70 lies between 11/16, equal to 0.6875, and 12/16, equal to 0.75. Nearest rounding selects 11/16 because its distance from 0.70 is 0.0125, while the distance to 12/16 is 0.05. The lower and upper results remain visible so you can inspect both choices rather than relying only on the final answer.
Rounding direction matters with negative numbers. “Round down” means toward negative infinity, so it can produce a more negative result. “Truncate” means toward zero. For instance, a negative scaled value of -3.7 rounds down to -4 but truncates to -3. The calculator labels the active rule and reports the signed difference to make this behavior clear.
Where sixteenths are useful
- Woodworking cuts and board dimensions
- Construction layouts and tape-measure readings
- Machining checks with fractional-inch specifications
- Fabrication, metalwork, and shop drawings
- Craft templates and material planning
- Quality-control tolerances and inspection records
Accuracy and tolerance
Rounding to the nearest sixteenth can introduce at most half a sixteenth of one unit under ordinary nearest rounding. That theoretical maximum is 1/32, or 0.03125. A tighter project may require thirty-seconds, sixty-fourths, decimal inches, or metric measurements instead.
Exact fraction versus sixteenth approximation
The exact fraction represents the decimal precisely when the entered value can be safely converted using integer arithmetic. For example, 0.7 is exactly 7/10. Its sixteenth approximation is 11/16, which equals 0.6875. Showing both values prevents the rounded shop measurement from being mistaken for the original mathematical quantity.
Decimal feet mode
Decimal feet should not be read as decimal inches. In 2.5 feet, the decimal portion 0.5 represents half a foot, which equals six inches. The feet-and-inches mode preserves the whole feet, multiplies the fractional foot by twelve, and then rounds the resulting inches to the nearest sixteenth. This is particularly helpful when survey, architectural, or estimating data is supplied in decimal feet but field measurements are taken with an inch-based tape.
Rounding method comparison
| Method | Behavior | Typical purpose |
|---|---|---|
| Nearest; halves upward | Selects the nearest integer after multiplying by 16. Exact positive halves move upward. | General measurement conversion. |
| Half away from zero | Exact halves increase the absolute magnitude for both positive and negative values. | Symmetric commercial-style rounding. |
| Half toward zero | Exact halves reduce the absolute magnitude. | Conservative magnitude handling in specialized workflows. |
| Banker’s rounding | Exact halves move to the nearest even integer. | Large datasets where cumulative rounding bias matters. |
| Always round down | Uses the mathematical floor of the scaled value. | Lower-bound material or clearance checks. |
| Always round up | Uses the mathematical ceiling of the scaled value. | Minimum coverage or allowance calculations. |
| Truncate | Removes the scaled fractional portion toward zero. | Workflows requiring no upward magnitude adjustment. |
Frequently asked questions
What is the nearest sixteenth to 0.3?
Multiply 0.3 by 16 to get 4.8. Nearest rounding gives 5, so the result is 5/16, equal to 0.3125.
Why does the simplified denominator sometimes change?
A fraction such as 8/16 and 1/2 names the same quantity. The calculator can retain denominator 16 for ruler comparison and also show the reduced form.
What happens when the numerator becomes 16?
Sixteen sixteenths equals one whole. The calculator carries that whole into the mixed-number portion, preventing results such as 2 16/16.
Can this calculator process negative measurements?
Yes. Negative signs are preserved, and the selected rounding method controls whether a result moves toward zero, away from zero, upward, or downward.
Is a sixteenth accurate enough for machining?
It depends on the specification. One sixteenth is 0.0625 inch, which is too coarse for many machining tolerances. Always follow the drawing and required precision.
How is percentage error calculated?
The calculator divides the absolute rounding error by the absolute original value and multiplies by 100. Percentage error is undefined when the original value is zero and the converted value is nonzero.
Can I use commas as decimal separators?
A single comma without a period is interpreted as a decimal separator. When commas and a period both appear, commas are treated as grouping separators.
Does scientific notation work?
Yes. Inputs such as 1.25e-1 and 2e3 are accepted when they fall within PHP’s finite numeric range.