Percent Decrease Calculator

Background.

A percent decrease calculator answers the mirror-image question to percent increase: by what percentage did this go down? Enter the old value and the new value and the page returns the percent decrease and the plain absolute drop, using arbitrary-precision decimal arithmetic so a figure like a $24 drop on a $150 stock price returns exactly 16%, not a floating-point approximation. Type a price before and after a markdown, a body weight before and after a diet, a reservoir level before and after a drought, or a headcount before and after layoffs, and the calculator handles the division for you.

Quanta already ships a general percentage-change calculator that reports a signed percent change alongside an absolute change and a symmetric percent-difference figure. This page is deliberately narrower, and for the same reason its sibling percent-increase calculator is narrower: "percent decrease" is one of the highest-volume directional percentage searches on the internet, typed by someone who already knows the value went down and wants a single, unambiguous, positive number describing how far it fell — not a negative sign they have to interpret, and not a mode selector standing between them and their answer.

That design choice — returning a positive number when a real decrease occurs — is a deliberate sign convention, and it is the opposite convention from the one used internally by the general percentage-change tool, which always reports growth as positive and decline as negative. Here, percentDecrease = (oldValue − newValue) ÷ |oldValue| × 100, which is precisely the negative of the percent-increase formula applied to the same two numbers. If a price falls from $150 to $126, percent-decrease reports +16%, while percent-increase (applied to the same two values) would report −16%. Both numbers describe the same event; this page's convention is simply the one that reads naturally to someone who already knows they're looking at a decline: "the price dropped by 16%" rather than "the price changed by negative 16%."

The formula divides by the old value, not the new value, and that choice has real consequences that trip up even experienced analysts. A price that falls from $100 to $80 has decreased by 20% (20 ÷ 100). To reverse that exact move — going back from $80 to $100 — requires a 25% increase (20 ÷ 80 × 100), not a 20% increase, because the base you're now working from is smaller. This asymmetry is the mathematical reason that recovering from any percentage loss always demands a proportionally larger percentage gain, and it shows up everywhere from investment portfolios (a 50% drawdown needs a 100% recovery gain) to weight-loss framing (losing 20% of your body weight and gaining it back is not simply reversing a 20% gain).

Because the formula divides by the old value, an old value of exactly zero makes percent decrease undefined — there is no percentage decline from nothing. The calculator throws a clear error rather than returning a misleading number in that case, the same defensive behaviour used across every percentage tool on this site. Negative starting values are still handled correctly: the absolute value of the old value sits in the denominator, so a quantity moving further from zero in the negative direction (say, a temperature deviation deepening from −50 to −80) is correctly reported as a positive percent decrease, because the underlying value genuinely got smaller.

Below the calculator you'll find the formula derivation with the sign convention spelled out explicitly, a hand-verified worked example using a real stock-price decline, and eight FAQs covering percentage points, negative results, price-drop math, and when to reach for the general percentage-change tool instead.

What is percent decrease calculator?

Percent decrease is the directional, signed measure of how much a value has fallen, expressed as a percentage of its original value, with the sign convention chosen so a genuine decline returns a positive number: percentDecrease = (oldValue − newValue) ÷ |oldValue| × 100. Like percent increase, it is grounded in the proportional-reasoning skills named explicitly in Common Core State Standard 7.RP.A.3, which lists "percent increase and decrease" alongside markups, markdowns, and simple interest as core applications of ratio and percent reasoning. A percent decrease calculation, like a percent increase calculation, always requires two ordered numbers: an old (earlier, starting, or baseline) value and a new (later, ending, or resulting) value, because the percentage only has meaning once you know which number the comparison is anchored to. The denominator is always the old value, never the new one, which is why a $20 drop on a $100 item (20%) and a $20 recovery back to $100 on an $80 item (25%) are different percentages despite the identical dollar amount — the base each percentage is measured against is different.

How to use this calculator.

1. 01Enter the old value — the starting number, before the decrease happened.
2. 02Enter the new value — the ending number, after the decrease happened.
3. 03Read the percent decrease. A positive number means the value fell by that percentage relative to the old value.
4. 04Read the absolute change for the plain dollar-or-unit drop between the two numbers.
5. 05If the percent decrease comes back negative, the value actually grew rather than fell — switch to the percent-increase calculator for a page framed around that direction, or use the general percentage-change tool if you want both directions handled with a single, symmetric sign convention.
6. 06Confirm which number you entered as "old" before trusting the result — the denominator is always the old value, so swapping the two inputs changes both the sign and the magnitude of the answer.

The formula.

The absolute change is oldValue minus newValue — a plain subtraction, kept in the original units, that comes out positive whenever the value genuinely fell. The percent decrease turns that same difference into a dimensionless ratio: divide the absolute change by the absolute value of the old value, then multiply by 100.

This calculator's sign convention is the mirror image of its sibling percent-increase page: percentDecrease(old, new) is always equal to −percentIncrease(old, new) for the same two numbers, because (oldValue − newValue) is the negation of (newValue − oldValue), and both formulas share the identical denominator |oldValue|. That relationship is enforced in the test suite and is worth internalizing: whichever of the two pages you land on, a real decline always produces a positive number here and a negative number on the percent-increase page, and a real increase produces the reverse.

Taking the absolute value of the old value in the denominator matters when the old value is negative. Consider a quantity moving from −50 to −80 — getting more negative, which for most real quantities (temperature deviation, account balance, elevation below sea level) represents a genuine worsening or decrease. Without the absolute value, (−50 − (−80)) ÷ (−50) × 100 = 30 ÷ −50 × 100 = −60%, which misleadingly reads as an increase. With the absolute value in place, (−50 − (−80)) ÷ |−50| × 100 = 30 ÷ 50 × 100 = +60%, correctly reporting a 60% decrease.

Because both formulas divide by the old value, oldValue = 0 remains the one input this calculator refuses, for the same reason it's refused on the percent-increase page: there is no honest percentage decline from a starting point of nothing. Note also that percent decrease and percent increase are not symmetric when chained: a value that falls 20% and then rises 20% does not return to its starting point, because the second percentage is calculated against the smaller, already-reduced base. $100 reduced by 20% is $80; $80 increased by 20% is $96, not $100 — the recovery gain needed to fully undo a 20% loss is actually 25%, not 20%.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Common Core State Standards for Mathematics, Grade 7, Ratios & Proportional Relationships, Standard 7.RP.A.3 — proportional relationships applied to multistep ratio and percent problems, explicitly naming percent increase and decrease.
2. [2]Common Core State Standards for Mathematics, Grade 6, Ratios & Proportional Relationships, Standard 6.RP.A.3(c) — finding a percent of a quantity as a rate per 100, the foundational skill percent decrease builds on.
3. [3]NIST Guide to the SI, Special Publication 811, §7.10.2 — rules and conventions for expressing relative differences as dimensionless percentages.
4. [4]Board of Governors of the Federal Reserve System — FAQ explaining the distinction between percentage points and percent change when describing rate movements.
5. [5]NIST Digital Library of Mathematical Functions, §4.2 — formal definitions of logarithm, exponential, and power relationships underlying ratio and proportional-decline arithmetic.