Enter a valid old value (cannot be zero).
The starting or reference value
Enter a valid new value.
The ending or current value
Percentage Change
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Sources & Methodology
Percentage change formula verified against CalculatorSoup, Omni Calculator, and standard mathematics curriculum references.
CalculatorSoup — Percentage Change Calculator
Standard formula: % Change = ((V2 − V1) ÷ |V1|) × 100. Uses absolute value of original value in denominator. Handles negative original values correctly.
Omni Calculator — Percentage Change
Key distinction: percentage change uses original value as reference point. Percentage difference uses average of two values. Positive = increase, negative = decrease.
GigaCalculator — Percentage Calculator
Percent change vs. percent difference distinction. Formula application for both positive and negative starting values. Use cases: business metrics, finance, statistics.
Formula: % Change = ((New Value − Old Value) ÷ |Old Value|) × 100. The |Old Value| means absolute value — always positive regardless of sign. If result is positive: percentage increase. If result is negative: percentage decrease. Undefined when Old Value = 0 (division by zero).
⏱ Last reviewed: April 2026
How to Calculate Percentage Change
Percentage change measures how much a value has increased or decreased relative to its original amount. It always has a reference point — the old value — which makes it different from percentage difference. The formula gives you a positive number for increases and a negative number for decreases.
The Percentage Change Formula
% Change = ((New Value − Old Value) ÷ |Old Value|) × 100
Worked examples:
Price from $80 to $100: ((100 − 80) ÷ 80) × 100 = +25% increase
Price from $100 to $75: ((75 − 100) ÷ 100) × 100 = −25% decrease
Temperature from −20 to 20: ((20 − (−20)) ÷ |−20|) × 100 = +200% increase
Sales from 500 to 650: ((650 − 500) ÷ 500) × 100 = +30% increase
Price from $80 to $100: ((100 − 80) ÷ 80) × 100 = +25% increase
Price from $100 to $75: ((75 − 100) ÷ 100) × 100 = −25% decrease
Temperature from −20 to 20: ((20 − (−20)) ÷ |−20|) × 100 = +200% increase
Sales from 500 to 650: ((650 − 500) ÷ 500) × 100 = +30% increase
Common Percentage Change Examples
| Scenario | Old Value | New Value | Change | Type |
|---|---|---|---|---|
| Stock price | $40 | $52 | +30% | Increase |
| Weight loss | 180 lbs | 162 lbs | −10% | Decrease |
| Salary raise | $60,000 | $66,000 | +10% | Increase |
| Sales drop | 1,200 units | 900 units | −25% | Decrease |
| Population | 10,000 | 13,500 | +35% | Increase |
| Gas price | $3.20 | $2.88 | −10% | Decrease |
| Doubled | 50 | 100 | +100% | Doubled |
| Tripled | 50 | 150 | +200% | Tripled |
Percentage Change vs Percentage Difference
| Feature | Percentage Change | Percentage Difference |
|---|---|---|
| Use when | One value is clearly older/baseline | Two values are equal in standing |
| Reference point | The old (original) value | Average of both values |
| Direction | + increase / − decrease | Always positive |
| Formula | (New − Old) ÷ |Old| × 100 | |V1 − V2| ÷ ((V1+V2)/2) × 100 |
| Example: 6 vs 9 | +50% (6 to 9) | 40% different |
💡 Common mistake: A 100% increase means the value doubled (not tripled). A 200% increase means it tripled. This is because 100% of the original was added to it. Similarly, a value can only decrease by a maximum of 100% (to zero) — something cannot decrease by more than 100% unless it goes negative, in which case the percentage change can exceed −100%.
Frequently Asked Questions
% Change = ((New Value − Old Value) ÷ |Old Value|) × 100. The |Old Value| means take the absolute value of the original (always positive). Positive result = increase. Negative result = decrease. Example: old=50, new=75: ((75−50)÷50)×100 = 50% increase.
Percentage change has a direction — it measures change FROM a specific old value TO a new value. The old value is always the reference. Percentage difference has no direction — it compares two equal-standing values using their average as reference. Use change when one value is clearly a baseline. Use difference when comparing two similar values.
Percent Increase = ((New − Old) ÷ Old) × 100 when New > Old. Example: $80 to $100: ((100−80)÷80)×100 = 25% increase. The result is always positive for an increase.
Percent Decrease = ((Old − New) ÷ Old) × 100 when Old > New. Example: $100 to $75: ((100−75)÷100)×100 = 25% decrease. Using the general formula you get −25%, which also means a 25% decrease.
Yes. 100% increase = doubled. 200% increase = tripled. 300% increase = quadrupled. Example: 50 to 200 = ((200−50)÷50)×100 = 300% increase. Decreases can also exceed 100% when going from positive to negative values. 50 to −50 = ((−50−50)÷50)×100 = −200%.
A negative result means the value decreased. Example: 100 to 80 = ((80−100)÷100)×100 = −20%. This is a 20% decrease. The magnitude tells you how much it changed; the negative sign confirms it went down.
Percentage change is undefined when the old value is zero (division by zero is impossible). In this case describe the change in absolute terms — the value went from 0 to X. You cannot express this as a percentage change.
Everywhere: stock prices and investment returns, salary negotiations, inflation tracking, business revenue growth month-over-month, population statistics, sports performance, weight loss tracking, and price comparison shopping. Any time you compare a new value to an old baseline, percentage change is the right metric.
New Value = Old Value × (1 + % Change ÷ 100). For 20% increase on $50: 50 × 1.20 = $60. For 20% decrease on $50: 50 × 0.80 = $40. For 150% increase on 100: 100 × 2.50 = 250.
Percentage change is relative: 10% to 15% is a 50% change ((15−10)÷10×100 = 50%). Percentage points are absolute: 10% to 15% is 5 percentage points. A central bank raising rates from 2% to 3% is 1 percentage point but a 50% percentage change in the rate. Always clarify which you mean in financial and economic contexts.
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