Percentage Change Formula: How to Calculate Increase and Decrease

Whether you are tracking a stock price, comparing this month’s sales to last month’s, or figuring out how much a price went up, you are calculating percentage change. The formula is short, but the sign and direction often trip people up. This guide walks through everything clearly.

The percentage change formula

Percentage Change = ((New Value − Old Value) / |Old Value|) × 100

The vertical bars around Old Value mean you use the absolute value (strip the negative sign if it is negative). The sign of the result tells you the direction:

• Positive result = increase
• Negative result = decrease

Percentage increase

Use this when the new value is greater than the old value.

Formula:

Percentage Increase = ((New − Old) / Old) × 100

Example: Price increase

A coffee shop raised the price of a latte from $4.00 to $4.80.

Percentage Increase = ((4.80 − 4.00) / 4.00) × 100
                    = (0.80 / 4.00) × 100
                    = 0.20 × 100
                    = 20%

The latte price increased by 20%.

Example: Salary raise

An employee earned $50,000 last year and earns $54,500 this year.

Percentage Increase = ((54,500 − 50,000) / 50,000) × 100
                    = (4,500 / 50,000) × 100
                    = 0.09 × 100
                    = 9%

Their salary increased by 9%.

Percentage decrease

Use this when the new value is less than the old value.

Formula:

Percentage Decrease = ((Old − New) / Old) × 100

This version gives a positive number representing the magnitude of the drop. Alternatively, you can use the general formula — you will just get a negative number, which also communicates the decrease.

Example: Retail discount

A jacket originally priced at $120 is now on sale for $90.

Percentage Decrease = ((120 − 90) / 120) × 100
                    = (30 / 120) × 100
                    = 0.25 × 100
                    = 25%

The jacket is 25% cheaper.

Example: Website traffic drop

A blog had 8,400 visitors in March and only 6,720 in April.

Percentage Change = ((6,720 − 8,400) / 8,400) × 100
                 = (−1,680 / 8,400) × 100
                 = −0.20 × 100
                 = −20%

Traffic decreased by 20%.

Step-by-step process

1. Identify the old value (starting point, baseline, original).
2. Identify the new value (ending point, current, updated).
3. Subtract: New − Old. Note the sign.
4. Divide by the old value (use absolute value if old value is negative).
5. Multiply by 100 to express as a percentage.
6. Interpret the sign: positive = increase, negative = decrease.

Worked examples at a glance

Scenario	Old Value	New Value	Change	% Change
Stock price up	$25.00	$31.25	+$6.25	+25%
Product price down	$80	$64	−$16	−20%
Population growth	1,200,000	1,320,000	+120,000	+10%
Monthly sales drop	$42,000	$37,800	−$4,200	−10%
Test score improvement	55	77	+22	+40%

What if the old value is zero?

The formula breaks down when the old value is zero because you cannot divide by zero. In practice this situation means you are starting from nothing and adding something — a 0-to-something change has no meaningful percentage representation. You would typically describe this as “went from zero to X” rather than as a percentage change.

If the old value is negative (for example, a company that went from a loss of $10,000 to a profit of $5,000), the formula still works mathematically, but the result is difficult to interpret intuitively. In those cases, many analysts simply note the change in absolute terms alongside the direction (e.g., “swung from a $10K loss to a $5K profit”).

Percentage change vs. percentage points

Suppose the unemployment rate drops from 6% to 4.5%.

• Percentage point change: 4.5 − 6 = −1.5 percentage points
• Percentage change: ((4.5 − 6) / 6) × 100 = −25%

Both statements are true, but they mean very different things. A 25% reduction in the unemployment rate sounds much more dramatic than a 1.5 percentage point reduction, yet both describe the same event. Always specify which you mean.

Chained percentage changes are not additive

If a price increases 20% and then decreases 20%, you might expect to be back where you started. You are not.

• Start: $100
• After +20%: $100 × 1.20 = $120
• After −20%: $120 × 0.80 = $96

A 20% increase followed by a 20% decrease leaves you at 96% of the original — a net loss of 4%. The reason is that each percentage is calculated on a different base. This matters for investment returns, pricing strategies, and any multi-step analysis.

Reverse percentage change: finding the original value

Sometimes you know the percentage change and the new value, and you need to find the original.

Formula:

Old Value = New Value / (1 + (% Change / 100))

Example: A price increased by 15% and is now $92. What was the original price?

Old Value = 92 / (1 + 0.15) = 92 / 1.15 = $80

For a decrease:

Old Value = New Value / (1 − (% Change / 100))

Example: After a 25% drop, a stock trades at $60. What was the original price?

Old Value = 60 / (1 − 0.25) = 60 / 0.75 = $80

Use the calculator

The formula is straightforward once you have the old and new values in hand, but it is easy to make arithmetic errors under pressure. Our percentage calculator handles percentage increase, percentage decrease, and reverse lookups in seconds — just enter two numbers and it does the rest.