Percent Decrease Calculator
Calculate the percentage decrease between two values, or find the reduced or original value from a percent off
By Waqar Mushtaq · Last updated:
A percent decrease expresses how much a value has fallen as a share of where it started -- "25% off," "down 12% from last year," "lost 8% of its weight." This calculator answers all three questions that come up with a decrease: how big was the drop (given the before and after values), what's left after a given percent off (given the original value and the percentage), and what the value was before a known percent decrease (given the reduced value and the percentage). Every result also shows the percent increase you'd need to get back to where you started, plus a table of the same original value at common percent decreases -- because a 50% drop takes a 100% gain to undo, which surprises people more often than you'd think.
How Percent Decrease Is Calculated
O(1) calculationV_original = starting value · V_new = value after the decrease
d = percent decrease as a decimal (25% = 0.25)
Percent increase needed to return from V_new to V_original
Subtract the new value from the original to get the amount of the decrease, divide by the original value, and multiply by 100. Always divide by the original value, not the new one -- that's the single most common mistake with percent decrease.
Example -- find the percent decrease: a jacket drops from $80 to $60. (80 − 60) / 80 × 100 = 20 / 80 × 100 = 25% decrease
Example -- find the value after a decrease: take 15% off $200. 200 × (1 − 0.15) = 200 × 0.85 = $170
Example -- find the original value: an item costs $45 after 40% off. 45 / (1 − 0.40) = 45 / 0.60 = $75
Why recovering takes more than the decrease: after a 25% drop, $80 becomes $60. Getting back to $80 means gaining $20 on a base of $60, which is 20 / 60 = 33.33% -- larger than the original 25% because the increase is measured from the smaller number.
If the "new" value is actually higher than the original, the formula returns a negative percent decrease, which is a percent increase -- see the Percent Change Calculator for working with both directions at once.
Use Cases
Sale Prices and Discounts
Work out the sale price after a percent-off discount, the real percentage off when a store only shows "was $X, now $Y," or the original price of something you only know the discounted price and percentage for.
Investment and Portfolio Drawdowns
A portfolio that falls 20% needs a 25% gain to break even, and one that falls 50% needs a 100% gain. The recovery column makes that asymmetry explicit, which is why drawdowns are usually discussed alongside the gain needed to recover from them.
Weight Loss and Fitness Tracking
Express weight lost, body-fat reduction, or a faster race time as a percentage of the starting value, so progress is comparable across people with different starting points.
Budget Cuts and Cost Reductions
Report spending reductions, energy-use savings, or headcount changes as a percent decrease from the baseline period -- or work out the target spend after a planned percentage cut.
Frequently Asked Questions
How do you calculate a percent decrease?
Subtract the new value from the original value, divide the result by the original value, and multiply by 100. For example, going from 80 to 60 is (80 − 60) / 80 × 100 = 25% decrease.
Why do I need a bigger percent increase to get back to the original value?
Because the increase is measured from the smaller, already-reduced value. A 50% decrease takes 100 down to 50; going from 50 back to 100 is an increase of 50 on a base of 50, which is 100%. In general, recovering from a decrease of d needs an increase of d / (1 − d).
How do I find the original price before a discount?
Divide the discounted price by (1 − the discount as a decimal). An item that costs $45 after 40% off was originally $45 / 0.60 = $75. A common mistake is adding 40% back onto $45, which gives $63 -- too low, for the same reason as the recovery question above.
Can a percent decrease be more than 100%?
Only if the value crosses below zero (for example, a profit of $100 turning into a loss of $50 is a 150% decrease). For quantities that can't go negative -- prices, weights, counts -- a 100% decrease means the value has dropped to zero, which is the maximum.
What is the difference between percent decrease and percentage points?
A percent decrease is relative to the starting value; a percentage-point change is the plain difference between two percentages. An interest rate falling from 5% to 4% is a 1 percentage-point drop but a 20% decrease (1 is 20% of 5).
Methodology
The formula above is implemented as a standalone module covered by unit tests, so its worked examples are re-checked on every change to the site. It is verified against the authoritative sources listed below.
Maintained by Waqar Mushtaq. Spotted a result that looks wrong? Report it and it becomes a failing test.