The percent change formula calculates how much a value has increased or decreased relative to its original amount, expressed as a percentage. It's used everywhere from finance and retail to science and everyday comparisons.

Percent change formula
% Change = (New Value − Old Value) ÷ Old Value × 100
A positive result = increase  ·  A negative result = decrease

You can also write it as:

(New − Old) / Old × 100

Or in fraction notation: [(New − Old) / Old] × 100. All three are identical — the notation changes but the equation does not.

What each part of the formula means

New Value
The final or current value
The number you ended up with — the price after the change, the salary after a raise, the score after revision.
Old Value
The original or starting value
Your baseline — what the value was before the change occurred. This is always the denominator.
÷ Old Value
Normalise against the baseline
Dividing by the old value makes the result relative — so a £50 change means something different starting from £100 vs £1,000.
× 100
Convert to a percentage
Multiplying by 100 converts the decimal into a percentage. Without this step you'd get 0.25 instead of 25%.

Step-by-step examples

Example 1 — Percentage increase (salary)

Salary rises from £32,000 to £36,800. What is the percentage increase?
1
Find the difference: 36,800 − 32,000 = 4,800
2
Divide by the old value: 4,800 ÷ 32,000 = 0.15
3
Multiply by 100: 0.15 × 100 = 15
(36800 − 32000) ÷ 32000 × 100 = +15% increase

Example 2 — Percentage decrease (sale price)

A jacket drops from £120 to £84. What is the percentage decrease?
1
Find the difference: 84 − 120 = −36
2
Divide by the old value: −36 ÷ 120 = −0.30
3
Multiply by 100: −0.30 × 100 = −30
(84 − 120) ÷ 120 × 100 = −30% decrease

Example 3 — Stock price change

A share bought at £4.50 is now trading at £5.85. What is the percentage gain?
1
Find the difference: 5.85 − 4.50 = 1.35
2
Divide by the old value: 1.35 ÷ 4.50 = 0.30
3
Multiply by 100: 0.30 × 100 = 30
(5.85 − 4.50) ÷ 4.50 × 100 = +30% gain

Example 4 — Negative starting value

A business had a loss (−£8,000) last year and a loss (−£5,000) this year. Did performance improve?
1
Find the difference: −5,000 − (−8,000) = 3,000
2
Divide by the old value: 3,000 ÷ −8,000 = −0.375
3
Multiply by 100: −0.375 × 100 = −37.5
(−5000 − (−8000)) ÷ −8000 × 100 = −37.5%

The formula gives −37.5%, which is mathematically correct but counterintuitive — the loss actually shrank, which is an improvement. When working with negative baselines, always sense-check the result in context rather than relying on the sign alone.

Formula variations

The core equation stays the same, but it's written differently depending on context.

Percent increase formula

(New − Old) ÷ Old × 100

Same formula — used when the new value is higher than the old. Result is always positive.

Percent decrease formula

(Old − New) ÷ Old × 100

Subtract in the opposite order to get a positive result for a decrease. Equivalent to the standard formula with the sign flipped.

Percentage change in price

(P2 − P1) ÷ P1 × 100

P1 = original price, P2 = new price. Used for stock prices, retail prices, and cost tracking.

Year-over-year (YoY) formula

(This Year − Last Year) ÷ Last Year × 100

Compares equivalent periods 12 months apart. Removes seasonal noise from the comparison.

Percent change in Excel

=(B1-A1)/A1*100

A1 = old value, B1 = new value. Format the cell as a number or percentage as needed.

Percent difference formula

|A − B| ÷ ((A+B) ÷ 2) × 100

Different equation — used when there is no clear "original" value. Symmetric: order doesn't matter. See our full comparison.

Percent change of a percentage

(New % − Old %) ÷ Old % × 100

When the values being compared are themselves percentages — interest rates, conversion rates, tax rates. See our full guide with examples.

Percentage variance (budget vs actual)

(Actual − Budget) ÷ Budget × 100

Same formula, different framing. Used in financial reporting to compare performance against a plan. See our percentage variance guide.

Percent change formula vs percent difference formula

These two are often confused. The key difference is what you divide by.

Percent change
Divides by the original value
(New − Old) ÷ Old × 100

Use when one value is clearly the starting point — before/after, old/new, baseline/result.
Percent difference
Divides by the average of both values
|A−B| ÷ ((A+B)÷2) × 100

Use when neither value is the baseline — two lab measurements, two survey results.

Common mistakes with the percent change equation

Dividing by the new value instead of the old

The old value is always the denominator. Dividing by the new value produces a different (incorrect) result. If a price goes from £50 to £75: correct is (75−50)÷50×100 = 50%. Using the new value gives (75−50)÷75×100 = 33.3% — wrong.

Forgetting to multiply by 100

Without ×100 you get a decimal ratio (0.50), not a percentage (50%). Both are mathematically equivalent but percentage is the expected format in almost every real-world context.

Thinking percent changes are reversible

A +50% increase followed by a −50% decrease does not return to the original. Starting at £100: +50% → £150, then −50% → £75. You need a +100% increase to reverse a −50% decrease.

Using the formula when the old value is zero

Division by zero is undefined — the formula breaks down entirely. If the original value is zero, describe the change in absolute terms instead (e.g. "grew from 0 to 200 units").

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Frequently asked questions

What is the percent change formula?

The percent change formula is: (New Value − Old Value) ÷ Old Value × 100. A positive result means an increase; a negative result means a decrease. The old value is always the denominator.

What is the percent change equation in simple terms?

Find how much the value changed (new minus old), then ask "what fraction of the original is that?" (divide by old), then convert to a percentage (multiply by 100). Three steps: difference, divide, scale.

Can the percent change formula give a result over 100%?

Yes. If a value doubles, that is a 100% increase. If it triples, that is a 200% increase. There is no upper limit — very large percentage changes occur when starting values are small and ending values are large.

How is percent change different from percent difference?

Percent change uses the original value as the denominator and is directional (positive or negative). Percent difference uses the average of both values and is always positive. Use percent change for before-and-after scenarios; use percent difference when comparing two independent measurements. See our full guide.

What is the percent change formula in Excel?

If your old value is in cell A1 and new value in B1, enter: =(B1-A1)/A1*100. This returns the percentage change as a number. Alternatively, format the cell as a percentage and use =(B1-A1)/A1 to skip the ×100.