Calculating a percentage change is straightforward when both numbers are positive. However, when you encounter negative values—such as a business moving from a net loss to a net profit—the standard percentage change formula can produce misleading or mathematically incorrect results.
The Problem with the Standard Formula
The traditional formula for growth is:
((New Value – Old Value) / Old Value) * 100
If the "Old Value" is negative, the denominator becomes negative. This flips the sign of your result. For example, if you go from -100 (loss) to +50 (profit), that is clearly positive growth. But the standard formula would show a -150% growth rate, which is logically incorrect.
The Correct Formula for Negatives
To fix this, mathematicians and financial analysts use the absolute value of the starting number in the denominator:
Growth Rate = ((New Value – Old Value) / |Old Value|) * 100
Real-World Examples
From Loss to Profit: If your company lost -50,000 last year and earned 10,000 this year:
((10,000 – (-50,000)) / |-50,000|) * 100 = 120% growth.
Reducing a Loss: If you lost -1,000 last month and only lost -200 this month:
((-200 – (-1,000)) / |-1,000|) * 100 = 80% growth (improvement).
Deepening a Loss: If you lost -100 and now lost -300:
((-300 – (-100)) / |-100|) * 100 = -200% growth (decline).
function calculateNegativeGrowth() {
var oldVal = parseFloat(document.getElementById('startingValue').value);
var newVal = parseFloat(document.getElementById('endingValue').value);
var resultDiv = document.getElementById('resultDisplay');
var percentSpan = document.getElementById('percentResult');
var explanation = document.getElementById('explanationText');
if (isNaN(oldVal) || isNaN(newVal)) {
alert("Please enter valid numeric values for both fields.");
return;
}
if (oldVal === 0) {
percentSpan.innerHTML = "Undefined";
explanation.innerHTML = "Growth rate cannot be calculated when the starting value is zero (division by zero).";
resultDiv.style.display = "block";
return;
}
// Correct formula for negative growth logic: (New – Old) / Abs(Old)
var difference = newVal – oldVal;
var absOld = Math.abs(oldVal);
var growthRate = (difference / absOld) * 100;
percentSpan.innerHTML = growthRate.toFixed(2) + "%";
if (growthRate > 0) {
explanation.innerHTML = "This represents a positive growth or improvement of " + growthRate.toFixed(2) + "%.";
percentSpan.style.color = "#27ae60";
} else if (growthRate < 0) {
explanation.innerHTML = "This represents a negative growth or decline of " + Math.abs(growthRate).toFixed(2) + "%.";
percentSpan.style.color = "#c0392b";
} else {
explanation.innerHTML = "There is no change in the value.";
percentSpan.style.color = "#2c3e50";
}
resultDiv.style.display = "block";
}