Percentage Change Calculator

Percentage Change Formulas

Percentage Change

Markup

Margin

Mark-up vs Margin Example

Product costs $60, sells for $100:

• Markup = (100 − 60) / 60 × 100 = 66.67%
• Margin = (100 − 60) / 100 × 100 = 40%

What Is Percentage Change?

Percentage change measures how much a value moved from an old (original) value to a new value, expressed as a fraction of the original and multiplied by 100. A positive result is a percentage increase; a negative result is a percentage decrease.

Note the absolute value in the denominator: using |Old| keeps the sign of the result honest when the old value is negative, so the direction of the change is never distorted.

How to Calculate Percentage Change

1. Subtract: New value minus Old value (this is the absolute change).
2. Divide by the absolute value of the Old value.
3. Multiply by 100.

Worked Example: Percentage Increase

A stock price rises from $100 to $150. What is the percentage increase?

• Change: 150 - 100 = 50
• Divide: 50 / 100 = 0.5
• Multiply: 0.5 x 100 = 50% increase

Worked Example: Percentage Decrease

A jacket is marked down from $80 to $64. What is the percentage decrease?

• Change: 64 - 80 = -16
• Divide: -16 / 80 = -0.2
• Multiply: -0.2 x 100 = -20%, i.e. a 20% decrease

Why Direction Matters

Percentage change is not symmetric. Going from $100 to $150 is a 50% increase, but going back from $150 to $100 is a 33.33% decrease — because each change is measured against a different starting value. From 3.50 to 2.625 is a -25% change, while the reverse move from 2.625 to 3.50 is a +33.33% change. Always check which value is the "old" one.

Percentage Change with Negative Numbers

When the old value is negative, dividing by its absolute value keeps the increase/decrease reading correct.

Worked Example: -25 to 25

• Change: 25 - (-25) = 50
• Divide by |old|: 50 / 25 = 2
• Result: 200% increase

Worked Example: -25 to -50

• Change: -50 - (-25) = -25
• Divide by |old|: -25 / 25 = -1
• Result: -100%, i.e. a 100% decrease (the value became more negative)

Reverse Calculation: Find the Original Value

If you know the new value and the percentage change, work backwards. A value after a p% increase equals old x (1 + p/100); after a p% decrease it equals old x (1 - p/100). Divide to recover the old value.

Worked Example

A price is $180 after a 20% increase. The original price was 180 / 1.20 = $150. Check: 150 x 1.20 = 180.

Applying a Percentage Change

To find the value after a change, multiply by 1 plus or minus the decimal form of the percentage:

A salary of $50,000 with a 10% raise becomes 50,000 x 1.10 = $55,000. The same salary with a 10% cut becomes 50,000 x 0.90 = $45,000.

Markup vs Margin: Which to Use

Both measure profit, but from different baselines:

Retail pricing usually starts from markup ("I need 50% markup on this item"); financial reporting usually talks about margin ("our gross margin is 40%"). Convert between them:

Check: a 66.67% markup gives 0.6667 / 1.6667 = 0.40, a 40% margin. A 40% margin gives 0.40 / 0.60 = 0.6667, a 66.67% markup.

Percentage Change vs Percentage Points

When the values themselves are percentages, say which one you mean. A rate moving from 8% to 10% rose by 2 percentage points, which is a 25% relative increase (2 / 8 x 100). Mixing these up is one of the most common errors in news headlines and financial reports.

Percentage Change vs Percentage Difference

Percentage change treats one value as the reference (order matters). Percentage difference compares two values of equal standing, dividing by their average instead:

Use percentage change for before/after measurements (price then and now). Use percentage difference for lab comparisons where neither reading is the "original".

Common Mistakes to Avoid

• Dividing by the new value: the baseline is always the old (original) value, not the new one.
• Ignoring the sign: a negative result means a decrease — do not just drop the minus sign.
• Assuming symmetry: +50% then -50% does not return to the start ($100 to $150 to $75).
• Confusing markup and margin: 66.67% markup is not 66.67% margin (it is 40% margin).
• Percentage points vs percent: an 8% to 10% move is 2 percentage points, not a 2% increase.
• Old value of zero: percentage change is undefined when the old value is 0, because division by zero is impossible. Report the absolute change instead.

Real-World Applications

Tips and Best Practices

• Name the baseline: say "up 20% from last year", not just "up 20%".
• Keep the sign in intermediate steps: decide increase vs decrease only at the end.
• Sanity-check the direction: new bigger than old must give a positive change.
• Use absolute change alongside: "+$50 (+50%)" is clearer than either alone.

Percentage Change Formula Variations

The same relationship solves for any missing piece:

Use a negative p for decreases: a 15% decrease uses (1 - 0.15) = 0.85.

More Worked Examples

Restaurant Tip

A $45 bill with an 18% tip. Tip = 45 x 0.18 = $8.10, so the total is $45 + $8.10 = $53.10.

Sales Tax

A $200 item with 8.5% sales tax. Final price = 200 x 1.085 = $217.

Test Score Improvement

A score rises from 72 to 90. Percentage change = (90 - 72) / 72 x 100 = 18 / 72 x 100 = 25% improvement.

Population Growth

A town grows from 12,000 to 13,500 residents. Change = 1,500; 1,500 / 12,000 x 100 = 12.5% growth.