Percentage Decrease Calculator

How percentage decrease works

Quick answer: subtract the final value from the initial value, divide by the initial value and multiply by 100. Going from 80 to 68 is (80 − 68) ÷ 80 × 100 = 15%.

Percentage decrease formula

This is the percentage decrease calculation formula. A positive result is a fall; a negative result means the value actually rose.

How to calculate percentage decrease

1. 1Subtract the final value from the initial value to get the drop.
2. 2Divide the drop by the initial value, not the final value.
3. 3Multiply by 100 and add the percent sign.

To calculate a decrease in percentage terms between two numbers, the starting value is always the base. From 100 to 80 is a 20% decrease, but a drop from 80 to 60 is 25%, because the same gap of 20 is measured against a smaller start.

Where percentage decrease is used

Calculating percentages decrease is routine for price drops, falling sales, population decline, weight loss and fuel costs, and a percentage reduction calculator answers exactly the same question. How do you calculate a decrease in percentage when the numbers come from a report? Pick the earlier figure as the initial value and the later figure as the final value, then follow the steps above. The percentage lets you compare a fall in a small series with a fall in a large one.

How to decrease a number by a percentage

To reduce a number by a percent, multiply it by 1 minus the percent as a decimal. Decreasing 240 by 15% is 240 × 0.85 = 204. The table below applies the same method to 500. This is the second mode of the calculator above.

A quick mental check

For a 10% decrease, move the decimal point one place left and subtract: 10% of 250 is 25, so the new value is 225. For 20%, double the tenth and subtract; for 25%, take off a quarter; for 50%, halve it. Use the check to catch a slipped decimal, and the calculator for awkward figures such as 7.5%.

A decrease cannot exceed 100%

A 100% decrease takes the value to zero, so nothing can fall further. A percentage increase has no such cap, which is one reason the two are not mirror images. A result above 100% can only happen when the final value is below zero, so check the inputs. For example, 50 to −10 is a 120% decrease. Entering the values the wrong way round gives a negative result, not one above 100%.

Why recovering takes a bigger rise

Because the base shrinks after a fall, winning back the loss needs a larger percentage on the lower value. A 20% decrease is undone by a 25% increase, a 50% decrease needs a 100% increase, and a 10% decrease needs 11.1%. The general rule is decrease ÷ (100 − decrease) × 100.

Successive decreases multiply

Two decreases in a row do not add. A 20% decrease followed by a 10% decrease leaves 0.80 × 0.90 = 0.72 of the original, which is 28% less in total, not 30%.

Percentage decrease vs reduction, drop, loss and percent off

Reduction, drop, decline and loss are different words for the same arithmetic, so a percent reduction calculator, a percentage loss calculator and a percent loss calculator all do exactly what this page does. Percent off is the same calculation applied to a shop price; see the percent off calculator for stacked discounts and sales tax.

Increase and decrease together

Here is how to calculate increase and decrease percentage when you do not know the direction in advance: use (final − initial) ÷ initial × 100 and read the sign. The percentage change calculator works as a percent increase and decrease calculator. When you know the value rose, use the percentage increase calculator.

Percentage decrease in Excel and Google Sheets

With the old value in A2 and the new value in B2, type =(A2-B2)/A2 or the shorter =1-B2/A2 and format the cell as a percentage. The Excel guide has copy-ready versions for increase, change and difference.

Percentage decrease examples

Decreasing 500 by each percentage from 10% to 90%:

Percentage decrease code

Both versions reproduce the examples above (15%, 5%, 20%, 25%, 10%, 7.5% and 1,050), reject non-numeric input, refuse a starting value of 0 and keep the decrease-by percent between 0 and 100.

JavaScript

1function finite(name, v) {2  if (typeof v !== "number" || !Number.isFinite(v)) throw new TypeError(`${name} must be a finite number`);3}4​5function share(percent) {6  finite("percent", percent);7  if (percent < 0 || percent > 100) throw new RangeError("percent must be between 0 and 100");8  return percent / 100;9}10​11export function percentDecrease(initial, final) {12  finite("initial", initial);13  finite("final", final);14  if (initial === 0) throw new RangeError("initial must not be 0: the decrease from zero is undefined");15  return ((initial - final) / Math.abs(initial)) * 100; // negative means the value actually rose16}17​18export function decreaseBy(value, percent) {19  finite("value", value);20  return value * (1 - share(percent));21}22​23export function recoveryIncrease(percentDecrease) {24  const s = share(percentDecrease);25  if (s === 1) throw new RangeError("a 100% decrease cannot be recovered by a percentage rise");26  return (s / (1 - s)) * 100;27}

Python

1from decimal import Decimal2import math3​4​5def _num(name, v):6    if isinstance(v, bool) or not isinstance(v, (int, float, Decimal)) or not math.isfinite(float(v)):7        raise ValueError(f"{name} must be a finite number")8    return Decimal(str(v))9​10​11def _share(percent):12    percent = _num("percent", percent)13    if percent < 0 or percent > 100:14        raise ValueError("percent must be between 0 and 100")15    return percent / 10016​17​18def percent_decrease(initial, final):19    initial, final = _num("initial", initial), _num("final", final)20    if initial == 0:21        raise ValueError("initial must not be 0: the decrease from zero is undefined")22    return (initial - final) / abs(initial) * 100  # negative means the value actually rose23​24​25def decrease_by(value, percent):26    return _num("value", value) * (1 - _share(percent))27​28​29def recovery_increase(percent_decrease):30    s = _share(percent_decrease)31    if s == 1:32        raise ValueError("a 100% decrease cannot be recovered by a percentage rise")33    return s / (1 - s) * 100

recoveryIncrease(20) returns 25 and recoveryIncrease(50) returns 100, the recovery figures above. Round only for display: in JavaScript, decreaseBy(500, 70) returns 150.00000000000003, so format results with toFixed(2). The Python version uses Decimal and avoids the artefact.

Privacy and input safety

Values are calculated in your browser. The numbers you enter are not sent to a server or stored.

• Fields accept numbers only. Text, empty fields, NaN and Infinity are rejected with a message, and nothing you type is ever evaluated as code.
• In the decrease-by mode the percent must be between 0 and 100. A decrease of more than 100% would give a negative value, so it is refused.
• A comma followed by exactly three digits is read as a thousands separator, so 1,200 is 1200. Any other comma is a decimal point, so 12,50 is 12.50, and a number starting with 0, such as 0,500, is read as a decimal. Mixed formats such as 1.234,5 and ambiguous entries such as 1,2,3 are refused instead of guessed. Spaces, including no-break spaces, between digit groups are ignored.

Common percentage decrease mistakes

Percentage decrease vs change vs increase vs percent off