How to Calculate Percentage Increase or Decrease

Percentage change always uses a starting value as the denominator:

Percent change = ((new − old) ÷ old) × 100

The result is a signed number. Positive means increase; negative means decrease. People often drop the sign and say “decreased 15%” instead of “−15%,” but the math is the same.

Worked examples

• Revenue $80,000 → $100,000: ((100000 − 80000) ÷ 80000) × 100 = +25%
• Price $50 → $40: ((40 − 50) ÷ 50) × 100 = −20%
• Users 1,200 → 1,500: ((1500 − 1200) ÷ 1200) × 100 = +25%
• Score 92 → 92: ((92 − 92) ÷ 92) × 100 = 0%

You can also think in multipliers: new = old × (1 + change/100). A +25% change multiplies by 1.25; a −20% change multiplies by 0.80.

For single-value modes like “what is 15% of 80?” see the percentage calculator guide. This guide stays on comparing two observed values over a before/after story.

Increase and decrease are the same formula with different signs and everyday wording.

• Increase: new is larger than old → positive percent change
• Decrease: new is smaller than old → negative percent change; report the absolute value when you say “decreased X%”

Increase example

Salary $48,000 → $52,800.

((52800 − 48000) ÷ 48000) × 100 = +10%. The raise is a 10% increase on the old salary.

Decrease example

Inventory 400 units → 340 units.

((340 − 400) ÷ 400) × 100 = −15%, or a 15% decrease.

Asymmetry you must remember

Going up 25% and then down 25% does not return you to the start. From 40 to 50 is +25%. From 50 back by 25% lands at 37.5, not 40. To reverse a +25% step you need a −20% step, because the base changed. Always recompute with the current baseline.

Retail “X% off” is decrease-style math with the list price as old. For cart and coupon workups, the discount calculator guide focuses on sale price from percent off.

A bare “12%” without direction is incomplete for decisions. Signed change, absolute difference, and the multiplier each answer a different follow-up.

Output	What it answers	Example (40 → 50)
Signed % change	Relative move from old	+25%
Absolute difference	Raw gap in original units	+10
Multiplier	Factor to apply to old to get new	1.25

Finance and ops teams often store the multiplier or growth factor because chaining periods is easier: multiply successive factors rather than adding percent changes. Two periods of +10% each compound as 1.10 × 1.10 = 1.21, or +21% overall — not +20%.

When you report results, pair the percent with the absolute move. “Up 100% from 2 to 4 orders” is true and small; “up 100% from 2 million to 4 million” is a different business story. The free percentage change calculator surfaces signed change, absolute difference, and multiplier so you do not have to juggle three formulas by hand.

Reverse problems give you a percent change and either the old or new value, then ask for the missing side.

Find the new value

new = old × (1 + r/100), where r is the signed percent change.

• Old 200, increase 15%: 200 × 1.15 = 230
• Old 200, decrease 15%: 200 × 0.85 = 170

Find the original (old) value

old = new ÷ (1 + r/100)

• Final price 85 after a 15% drop: old = 85 ÷ 0.85 = 100
• Headcount 330 after +10% growth: old = 330 ÷ 1.10 = 300

Find the percent when both values are known

That is the standard change formula again: ((new − old) ÷ old) × 100.

Reverse math fails when someone treats “increased by 20% to reach 120” as subtract 20 instead of divide by 1.20. Always undo multiplication with division by the factor, not by subtracting the same percent of the new value.

General reverse-percentage skills also appear in “price before tax” style questions in the percentage calculator guide.

These two phrases get swapped in slides and headlines. They are not the same operation.

• Percentage change — directional; denominator is the old (baseline) value
• Percentage difference — usually symmetric; denominator is the average of the two values; no designated start

Same pair, three answers

A = 40, B = 50.

• Change 40→50: +25%
• Change 50→40: −20%
• Difference (|50−40| / 45 × 100): ≈ 22.22%

Use change when you can say “from last period to this period” or “before treatment vs after.” Use difference when two measurements are peers (two sensors, two quotes) and neither is the baseline. Deep comparison lives in the percentage difference guide and the matching percentage difference calculator.

Also separate percentage points: support from 40% to 50% is +10 points, which is a +25% relative change on the 40% base. “Up 10%” vs “up 10 points” are different claims.

Pick percentage change when time order or a clear baseline exists.

Situation	Prefer	Why
Month-over-month sales	Change	Old month is the base
Weight before/after a program	Change	Starting weight is baseline
Stock price return	Change	Buy price → sell price
Two lab instruments, same sample	Difference	No natural “old”
Inflation over a year	Change (index)	Price level path; see inflation tools
Coupon off list price	Change / discount	List is the base

Price-level paths over years often need CPI-style math rather than a single two-point hand calculation. For multi-year purchasing power, see the inflation calculator guide.

Near-zero bases inflate percents: 1 → 2 is +100% with only one unit of absolute change. Always show absolute units beside huge relative moves so readers are not misled.

Enter old and new in the correct order, confirm the mode is change (not difference), and read the labeled outputs.

1. Open the free percentage change calculator.
2. Enter the baseline as the old (or “from”) value.
3. Enter the comparison as the new (or “to”) value.
4. Read signed percent change, absolute difference, and multiplier.
5. For reverse mode, enter the known percent and the known side (old or new).
6. Copy wording that states direction: “increased 12% from A to B.”

Common mistakes

• Dividing by the new value — standard change divides by old
• Adding successive percent changes — compound with multipliers instead
• Calling difference “change” in a time series
• Confusing points with relative percent when both numbers are already rates
• Reversing a discount by subtracting percent of the sale price — divide by the factor

For everyday of/what-percent modes, use the percentage calculator. For symmetric gaps, use the percentage difference calculator. This guide is educational; regulated reporting and academic rubrics may mandate a specific definition — follow that when it conflicts with a general tool.