Permille to Decimal and Meter Converter
Convert a permille (‰) value to a decimal, or find its equivalent distance in meters over 1 km. Enter the value and choose a result under Convert to.
Convert Permille to Decimal or Length
Permille to Decimal and Meter Formula
Where:
- \(P\) — the value in permille (‰).
- \(D\) — the corresponding decimal value, with no unit.
- \(\Delta h\) — the distance in meters represented by that ratio over a 1 km baseline.
Permille means parts per thousand, so dividing by 1,000 gives the decimal ratio. Applying that ratio to 1 km (1,000 m) gives the meter result; this calculator does not accept a different baseline length.
Permille to Decimal and Meter – Calculation Example
Example: Enter the default Value of 5‰ and leave Convert to set to Decimal.
\[D=\frac{5}{1000}=0.005\]
Result: 0.005, with no unit. If you instead select Meter (for 1 km), the same 5‰ ratio gives \(0.005\times 1000\,\mathrm{m}=5\,\mathrm{m}\), so the result is 5 m.
How to use the calculator
- Enter a nonnegative number in Value. The field is measured in permille (‰); for example, enter 5 for 5‰, not 0.005.
- Under Convert to, choose Decimal to get a unitless ratio, or Meter (for 1 km) to apply that ratio to exactly 1 km.
- Read the Converted Value. The decimal option shows a number without a unit; the meter option shows a number followed by m.
To compare a permille value with a percentage, divide the permille number by 10: 5‰ equals 0.5%. If you need the distance in another unit after choosing meters, use the meters to feet converter.
What a permille conversion means
Permille, written ‰, expresses a ratio out of 1,000. A value of 1‰ means one part for every 1,000 parts of the same whole. It is dimensionless: 5‰ is the ratio 5/1,000, or 0.005. Unlike the percent sign (%), which means parts per hundred, the permille sign uses a thousand as its denominator. This makes small ratios convenient to write without several leading zeros.
The decimal result is useful when a calculation expects a multiplier rather than a value marked ‰. For example, a 5‰ share of a quantity is found by multiplying that quantity by 0.005. The calculator converts the ratio only; it does not calculate a share of an amount that you enter separately. For larger values, the same rule still applies: 1,000‰ equals 1 as a decimal, or 100%.
The meter result has a narrower meaning. It applies the permille ratio to a fixed distance of 1 km, which equals 1,000 m. For example, a 5‰ slope corresponds to a 5 m elevation change over 1 km of horizontal distance. The meter figure can also describe another proportional distance over a 1 km baseline, but only when the original permille value represents a distance ratio. A concentration of 5‰ does not, by itself, describe 5 m of anything.
Assumptions and practical limits
- The baseline is fixed. Meter (for 1 km) always uses 1,000 m. For a different baseline, multiply the decimal result by your chosen distance in meters. At 5‰ over 200 m, the proportional distance is \(0.005\times 200=1\,\mathrm{m}\).
- Use matching definitions of distance. In a slope calculation, the usual interpretation is elevation change divided by horizontal distance, not distance measured along the sloping surface. Check how the source of your permille figure defines its baseline.
- Only nonnegative input is accepted. The Value field has a minimum of zero. For a downhill slope, you can convert its nonnegative magnitude and describe the direction separately.
- Displayed precision is limited. Decimal results are rounded to four decimal places, while meter results are rounded to two. A very small nonzero ratio may therefore display as 0 in Decimal mode; that display does not mean the original value is zero.
The word “milli” in metric units also refers to a factor of one thousandth, but a metric prefix attached to a unit is not the same thing as a permille ratio. For unit scaling rather than parts-per-thousand ratios, use the metric prefix converter.
Frequently Asked Questions
How do I convert a decimal or percentage back to permille?
Multiply a decimal ratio by 1,000 to get permille. For example, \(0.012\) becomes \(12‰\). If you start with a percentage, multiply it by 10: \(1.2\%\) becomes \(12‰\). Check whether your starting number is a decimal or a percentage before multiplying; confusing the two produces a result that is 100 times too large or too small.
Is a 10‰ slope the same as a 10° slope?
No. A 10‰ grade has a rise-to-horizontal-run ratio of \(0.01\), giving an angle of \(\arctan(0.01)\), or about \(0.57°\). Degrees measure an angle, while permille expresses a ratio. Treating the two as interchangeable can substantially overstate the steepness of a road, railway, or path.
Does 1‰ of slope mean 1 mm of rise per meter?
Yes. For a slope measured against horizontal distance, 1‰ corresponds to 1 mm of elevation change per 1 m of horizontal travel. The same grade corresponds to 1 m of elevation change per 1 km. This is a useful way to check the scale of a result without converting the entire route to kilometers.
What if my distance is measured along the slope rather than horizontally?
Do not multiply the sloping distance directly by the grade ratio if you need an exact elevation change. With grade ratio \(r=P/1000\) and sloping length \(L\), the rise is \(Lr/\sqrt{1+r^2}\). At gentle grades, multiplying \(L\) by \(r\) is a close approximation, but the difference grows on steeper slopes.
Can a permille value be greater than 1,000‰?
Yes, but its meaning depends on the ratio. A slope above 1,000‰ has a rise greater than its horizontal run, so it is mathematically possible. A share of a fixed whole, however, cannot exceed 1,000‰ unless the underlying quantity exceeds that whole. Check what the numerator and denominator represent before interpreting a large value.
Why does a small nonzero permille value display as zero?
The display rounds decimal results to four places and meter results to two. For example, \(0.01‰\) is a nonzero decimal ratio of \(0.00001\), but it displays as 0.0000 in Decimal mode. For more precision, divide the original permille value by 1,000 yourself rather than using the rounded display as the exact value.