How this instrument works
Percentage decrease measures how far a value fell, expressed as a share of where it started: (old − new) ⁄ old × 100. It is not a separate piece of mathematics from percentage change — algebraically it is the same ratio with the subtraction reversed, old minus new instead of new minus old — but it is a distinct instrument, because it enforces a direction the general formula does not. Feed it a new value that is larger than the old one and the sheet will not silently compute a negative-looking answer; it checks the order first and flags the pair as an increase, since a decrease is one-directional by definition.
The point of fixing the direction is that it matches how a fall is normally reported. A 25% pay cut, a 30%-off sale tag, a lake that has lost 40% of its surface area — none of these are stated with a minus sign in ordinary speech, even though the underlying arithmetic, run through the signed percentage-change formula, would come out negative. This instrument returns that same magnitude as a plain positive percentage, because 'percentage decrease' already carries the direction in its own name; asking the reader to also track a sign would just repeat information the label already gives.
The formula's two extremes are worth knowing. When new equals old, the numerator vanishes and the decrease is exactly 0% — nothing fell. When new reaches 0, the value has been wiped out entirely and the decrease hits its ceiling of 100%, since (old − 0) ⁄ old always equals 1. Because the new value here cannot go negative, 100% is the largest drop the formula will ever report; there is no meaning here to 'more than everything' disappearing.
- Enter the starting figure into Old value — the larger number and the base every drop is measured against.
- Enter the lower, later figure into New (smaller) value; the sheet expects this to be less than Old value.
- Read Percentage decrease: always a positive figure, showing how large the fall is relative to where it started.
- If New (smaller) value comes out larger than Old value, the sheet flags it — that pairing is an increase, and belongs on a percentage-increase or percentage-change sheet instead.
Worked example — a price cut from 100 to 75
A jacket is marked down from an old value of 100 to a new value of 75. Percentage decrease divides the fall by where the price started: (100 − 75) ⁄ 100 × 100 = 25 ⁄ 100 × 100 = 25%. The full arithmetic uses 100, the original price, as the base, so the 25-unit markdown reads as a clean 25% decrease — the same figure a sale tag would print.
Check the formula's edges against that same pair. Nothing falls if the price stays at 100: (100 − 100) ⁄ 100 × 100 = 0%, the baseline this sheet reports for no movement at all. Flip the entered figures instead, old at 75 and new at 100, and the sheet declines the pairing outright: 100 is larger than 75, which describes a rise, not a fall, and belongs on a different instrument.
Questions
How is percentage decrease different from percentage change?
Percentage change, (new − old) ⁄ old × 100, accepts either direction and returns a signed answer — negative for a fall, positive for a rise. Percentage decrease is the same ratio written the other way round, (old − new) ⁄ old × 100, and it expects new to be the smaller figure; that swap flips the sign so a fall is reported as a plain positive number, matching how a discount or a pay cut is normally spoken about.
Why does the calculator reject a new value larger than the old value?
Because that pairing is not a decrease. If new exceeds old, the value rose rather than fell, and old minus new would be negative — a negative 'decrease' is a contradiction in terms. The sheet checks the order first and flags the mismatch rather than returning a misleading figure; that same pair belongs on a percentage-increase or percentage-change sheet instead.
Can percentage decrease ever exceed 100%?
Not with these fields, no. New value has a floor of 0, and the largest possible fall is losing the entire original amount: (old − 0) ⁄ old × 100 = 100%. A '150% decrease' is not meaningful for an ordinary quantity, since there is nothing left below zero for it to fall further from — that phrase usually signals a different kind of measurement, not this one.
What is the difference between a percentage decrease and a percentage-point decrease?
A percentage decrease is a ratio: how big the fall is relative to the starting value. A percentage-point decrease is plain subtraction between two numbers that were already percentages. An interest rate falling from 6% to 4% dropped 2 percentage points, but in percentage-decrease terms that same move is (6 − 4) ⁄ 6 × 100 ≈ 33.3%, since it is measured against the original 6%, not against 100.
Why does the old value have to stay above zero?
Because old sits in the denominator, and dividing by zero has no defined result. A quantity that started at nothing has no base to measure a fall against — there is no way to say how much of zero has been lost. This sheet keeps Old value above zero so the ratio always has a real base to divide by.
What is the most common mistake people make computing this by hand?
Dividing by the wrong number — using the new, smaller value as the base instead of the original one. Dropping from 80 to 60 is a 20-unit fall; divided by the correct base, old = 80, that is (80 − 60) ⁄ 80 × 100 = 25%. Divide by the smaller new value instead and the same fall wrongly reads as 20 ⁄ 60 × 100 ≈ 33.3%, overstating the drop by measuring it against the wrong end of the change.