A percentage represents a value relative to 100. In scientific analysis, engineering, and statistics, it is often necessary to express these values as different types of rates (such as decimals or per-mille units) to simplify calculations or match industry standards.
Mathematical Formula
The fundamental conversion relies on the base of 100. To convert a percentage to a decimal rate:
Decimal Rate = Percentage / 100
Once you have the decimal rate, you can derive other formats:
Per Mille (‰): Multiply the decimal rate by 1,000.
Basis Points (BPS): Multiply the decimal rate by 10,000.
Ratio: Divide 1 by the decimal rate to find the "1 in X" frequency.
Example Calculation:
If you have a percentage of 0.5%:
1. Decimal Rate: 0.5 / 100 = 0.005
2. Per Mille: 0.005 × 1,000 = 5‰
3. Basis Points: 0.005 × 10,000 = 50 BPS
4. Ratio: 1 / 0.005 = 200 (Result: 1 in 200)
Common Conversions Table
Percent
Decimal
Per Mille
1%
0.01
10‰
0.1%
0.001
1‰
25%
0.25
250‰
function gcd(a, b) {
return b ? gcd(b, a % b) : a;
}
function calculateRate() {
var percentVal = document.getElementById('percentageInput').value;
if (percentVal === "" || isNaN(percentVal)) {
alert("Please enter a valid numeric percentage.");
return;
}
var p = parseFloat(percentVal);
var decimal = p / 100;
// Decimal Rate
document.getElementById('decimalResult').innerText = decimal.toLocaleString(undefined, {minimumFractionDigits: 0, maximumFractionDigits: 10});
// Per Mille
var permille = decimal * 1000;
document.getElementById('permilleResult').innerText = permille.toFixed(4).replace(/\.?0+$/, "") + " ‰";
// Basis Points
var bps = decimal * 10000;
document.getElementById('basisPointsResult').innerText = bps.toFixed(2).replace(/\.?0+$/, "") + " BPS";
// Ratio
if (decimal !== 0) {
var ratio = 1 / decimal;
document.getElementById('ratioResult').innerText = "1 in " + ratio.toLocaleString(undefined, {maximumFractionDigits: 2});
} else {
document.getElementById('ratioResult').innerText = "N/A";
}
// Fraction Calculation
if (decimal !== 0) {
var len = percentVal.toString().split('.')[1] ? percentVal.toString().split('.')[1].length : 0;
var denominator = Math.pow(10, len + 2);
var numerator = Math.round(p * Math.pow(10, len));
var common = gcd(numerator, denominator);
document.getElementById('fractionResult').innerText = (numerator / common) + " / " + (denominator / common);
} else {
document.getElementById('fractionResult').innerText = "0";
}
// Show results
document.getElementById('rateResults').style.display = "block";
}