How the math works
Methodology
The percentage decrease formula never changes — only which value is unknown:
percentage decrease = ( original − new ) ÷ original × 100
The multiplier shortcut
To apply a decrease p in one step, multiply by (1 − p/100). A 20% decrease means × 0.80; $100 × 0.80 = $80. To reverse it — recover the original from the new value — divide instead: $80 ÷ 0.80 = $100.
Sequential decreases multiply, they don't add
Each discount applies to the already-reduced value: final = original × (1 − p₁/100) × (1 − p₂/100) × …. So 30% then 20% gives × 0.70 × 0.80 = × 0.56, an effective 44% decrease — not 50%.
Honest edge cases
- New value higher than original? That's an increase, not a decrease — the calculator says so and shows the increase % instead of a misleading negative.
- Original value of zero? Division by zero is undefined; the calculator refuses rather than inventing a number.
- 100% decrease lands exactly at zero. Anything "more than 100%" needs negative numbers — a different formula.
- Rounding: results display with up to 2 decimals; internal math keeps full precision.
Questions, answered
Percentage decrease FAQ
What is the formula for percentage decrease?
Percentage decrease = ((Original value − New value) ÷ Original value) × 100. Example: a price falls from $100 to $80. (100 − 80) ÷ 100 × 100 = 20%. The calculator above shows every step of this working automatically, including the amount decreased and what fraction remains.
How to calculate percentage decrease between two numbers?
Use three steps. 1) Subtract: Original − New = amount decreased. 2) Divide the amount decreased by the original value. 3) Multiply by 100. Example: 600 down to 100 → (600 − 100) ÷ 600 × 100 = 83.33%. Enter both numbers in the calculator's Decrease mode to see the full working.
How do I calculate percentage decrease in Excel or Google Sheets?
Put the original value in A1 and the new value in B1, then use =(A1-B1)/A1 and format the cell as Percentage. The same formula works in Google Sheets. Example: A1 = 2500, B1 = 1400 → =(2500-1400)/2500 = 44%. If the result is negative, the value actually increased.
How do I work out percentage decrease on a calculator?
Type the original value, press minus, type the new value, press equals — that is the amount decreased. Then divide by the original value and press equals, then multiply by 100. Example on any pocket calculator: 100 − 80 = 20, then 20 ÷ 100 = 0.2, then × 100 = 20% decrease.
What is the difference between percentage decrease and percentage points?
They measure different things. A fall from 50% to 40% is a drop of 10 percentage points, but a 20% percentage decrease (10 ÷ 50 × 100). Percentage points are the simple arithmetic difference; percentage decrease is always relative to the starting value. Mixing them up is one of the most common statistics mistakes in news headlines.
Can a percentage decrease be more than 100%?
No — not for a single decrease from a positive starting value. A 100% decrease takes you exactly to zero, and you cannot go below zero without the numbers turning negative. Claims of a '150% decrease' are a red flag: the writer almost certainly confused percentage decrease with percentage points, or the values went negative (which needs the signed percent-change formula instead).
What if the new value is higher than the original value?
Then it is not a decrease at all — it is an increase, and this calculator will tell you so honestly instead of showing a negative percentage. Example: 80 rising to 100 is a 25% increase ((100 − 80) ÷ 80 × 100). For values that move in either direction, including through zero or into negatives, use a signed percent change calculator instead.
How do you reverse a percentage decrease to find the original value?
Divide the new value by (1 − p/100), where p is the percentage decrease. Example: after a 20% decrease the price is $80, so the original was 80 ÷ (1 − 0.20) = 80 ÷ 0.8 = $100. Use the 'Find original value' mode above and it does this reverse calculation for you, showing each step.
Why isn't 30% off then another 20% off the same as 50% off?
Because each discount applies to the already-reduced price, not the original. A 30% discount turns $100 into $70, then 20% off $70 is $14 more off — final price $56. Total effective decrease: (100 − 56) ÷ 100 = 44%, not 50%. Try the Sequential mode above: enter 30 and 20 to see both steps and the combined 44%.
What is a percentage decrease multiplier?
The multiplier is (1 − p/100). For a 20% decrease the multiplier is 0.80: just multiply the original value by 0.80 to get the new value ($100 × 0.80 = $80). Multipliers also chain neatly — a 30% then 20% decrease is × 0.70 × 0.80 = × 0.56, i.e. 44% off total.
How do you calculate percentage decrease year over year?
Use the decrease formula with last year as the original: ((Last year − This year) ÷ Last year) × 100. Example: sales of 2,500 units last year and 1,400 this year → (2500 − 1400) ÷ 2500 × 100 = 44% year-over-year decrease. If this year is higher, the same inputs give you the increase percentage instead.
What is the difference between percentage decrease, percent change, and percent difference?
Percentage decrease is directional and only handles falls: original down to a smaller new value. Percent change is the signed generalist — it handles rises and falls, including zero and negative numbers. Percent difference is symmetric: it compares two numbers with neither treated as the starting point. Percentage increase is the mirror image of this tool, for rises only. The comparison box above links to each specialist so you always land on the right formula.
Is there a shortcut to find the new value after a percentage decrease?
Multiply the original by (1 − p/100) in one step. For a 15% decrease, multiply by 0.85. Example: $200 × 0.85 = $170. That single multiplication replaces the subtract-divide-multiply routine, and it is exactly what the 'Find new value' mode computes.
How do you calculate a sale discount as a percentage decrease?
Treat the list price as the original and the sale price as the new value: (List price − Sale price) ÷ List price × 100. Example: a jacket marked down from $200 to $150 → (200 − 150) ÷ 200 × 100 = 25% off. The 'show your work' steps in the calculator lay this out exactly as a receipt would.