Percentage Increase Calculator
The percentage increase calculator finds the rise between a starting and a final value as a percentage, or adds a percent to any number. It also covers the percent increase formula, calculating increase percentages and compounding.
Example values are filled in. Replace them with your own.
Percentage increase
25%
Increase
Working
- 100 − 80 = 20
- 20 ÷ 80 × 100 = 25%
- Amount of the increase
- 20
- Fall needed to get back to the start
- -20%
This is a relative change, a share of the starting value. If both values are rates, the gap between them is measured in percentage points, a different measure. See the percentage points calculator.
Your rent goes from $1,450 to $1,595. Is that a 10% rise or a 9% one? The answer depends on which number you divide by, and it is easy to pick the wrong one.
Enter the starting value and the new value into this percent increase calculator and it returns the percentage increase with the working shown. The percentage increase calculator also has a second mode: enter a number and a percent and it adds the percent for you, so 240 plus 15% comes to 276.
How percentage increase works
Quick answer: subtract the starting value from the new value, divide by the starting value and multiply by 100. Going from 80 to 100 is (100 − 80) ÷ 80 × 100 = 25%.
Percentage increase formula
percentage increase = (final value - initial value) / abs(initial value) * 100This percent increase formula uses absolute-value bars around the initial value, which only matter when the start is negative; for ordinary positive values you can ignore them.
How to calculate percentage increase
- Subtract the initial value from the final value to get the increase.
- Divide the increase by the initial value, not the final value.
- Multiply by 100 and add the percent sign.
The starting value is always the base. That is why 80 to 100 is a 25% increase while the reverse move, 100 to 80, is a 20% decrease: the gap is 20 both times, but the base differs. For falls, use the percentage decrease calculator.
A quick way to calculate percent increase in your head
How do you calculate percentage increase without a calculator? Find 10% of the starting value by moving the decimal point one place, then count how many of those tenths the rise contains. From 48 to 60, a tenth of 48 is 4.8 and the rise is 12, which is 2.5 tenths, so the increase is 25%. Use the mental check to catch a slipped decimal, and the calculator for the exact figure.
How to increase a number by a percentage
To add a percent to a number, multiply by 1 plus the percent as a decimal. Adding 15% to 240 is 240 × 1.15 = 276. This is the second mode of the calculator above.
Increases over 100%
There is no cap. A 100% increase doubles a value and a 200% increase triples it. Going from 2,000 to 5,000 followers is a 150% increase, because the new value is 2.5 times the old one.
Compound increases: two rises are not one added rise
When an increase repeats, each rise applies to the already-increased value, so the percentages do not add. A 10% rise followed by another 10% multiplies by 1.10 × 1.10 = 1.21, which is 21%. Three yearly increases of 5% give 1.05³ − 1 = 15.76%, not 15%. The compoundIncrease function in the code section below does this for any number of periods. To work back to an annual percentage increase, take the nth root: 1,000 growing to 1,500 over 3 years is 1.5^(1/3) − 1 = 14.47% a year.
Percentage increase of a percentage
When the values are themselves percentages, such as a rate rising from 4% to 5%, two answers are both correct. The rise is 1 percentage point, and the relative increase is (5 − 4) ÷ 4 = 25%. State which one you mean. The percentage points guide covers the difference in full.
Zero and negative starting values
From a starting value of 0 the percentage increase is undefined, because the division fails. Report the absolute change instead. For a negative start, the calculator divides by the absolute value of the start, so −50 to −25 is +50%. Tools that divide by the signed start return −50% for the same move; the percentage change calculator explains the convention.
Percentage increase in Excel and Google Sheets
With the old value in A2 and the new value in B2, type =(B2-A2)/A2 and format the cell as a percentage. To add a percent instead, with the percent in B2, type =A2*(1+B2). The Excel guide covers copy-ready versions of these formulas for increase, change and difference.
Where percentage increase is used
Pay rises, rent reviews and price changes are the everyday cases: calculating increase percentages shows whether a raise beats inflation or whether a supplier's new quote is fair. Businesses track revenue, sales, traffic and sign-ups the same way, month on month or year over year. A percent growth calculator or percentage growth calculator does the same job, because a growth rate is a percentage increase measured over a period, and the same sum gives a percentage gain on an investment or a percentage improvement in a test score. The % increase calculator above works for any unit, since the units cancel in the division.
Percentage increase examples
Adding common percentages to 200:
| Percent added | Increase | New value |
|---|---|---|
| 5% | 10 | 210 |
| 10% | 20 | 220 |
| 20% | 40 | 240 |
| 25% | 50 | 250 |
| 50% | 100 | 300 |
| 100% | 200 | 400 |
Example 1: salary rise from $52,000 to $56,160
Given
Step 1
The increase is 56,160 − 52,000 = 4,160.Step 2
Divide by the starting salary: 4,160 ÷ 52,000 = 0.08.
Answer
Example 2: price rise from $4.50 to $5.40
Given
Step 1
The increase is $0.90, and 0.90 ÷ 4.50 = 0.20.
Answer
Example 3: population growth from 8,400 to 9,114
Given
Step 1
The increase is 714 people, and 714 ÷ 8,400 = 0.085.
Answer
Example 4: rent rise from $1,450 to $1,595
Given
Step 1
The increase is $145 a month, and 145 ÷ 1,450 = 0.10.
Answer
Example 5: followers from 2,000 to 5,000
Given
Step 1
The increase is 3,000, and 3,000 ÷ 2,000 = 1.5.
Answer
Example 6: raise a $120,000 budget by 5.2%
Given
Step 1
This is the second mode.
Answer
Percentage increase code
Both versions reproduce the examples above (8%, 20%, 8.5%, 10%, 150%, $126,240 and the 15.76% compound figure), reject non-numeric input and refuse a starting value of 0.
JavaScript
function finite(name, v) { if (typeof v !== "number" || !Number.isFinite(v)) throw new TypeError(`${name} must be a finite number`);}export function percentIncrease(initial, final) { finite("initial", initial); finite("final", final); if (initial === 0) throw new RangeError("initial must not be 0: the increase from zero is undefined"); return ((final - initial) / Math.abs(initial)) * 100;}export function increaseBy(value, percent) { finite("value", value); finite("percent", percent); return value * (1 + percent / 100);}export function compoundIncrease(percentPerPeriod, periods) { finite("percentPerPeriod", percentPerPeriod); finite("periods", periods); return ((1 + percentPerPeriod / 100) ** periods - 1) * 100;}Python
from decimal import Decimalimport mathdef _num(name, v): if isinstance(v, bool) or not isinstance(v, (int, float, Decimal)) or not math.isfinite(float(v)): raise ValueError(f"{name} must be a finite number") return Decimal(str(v))def percent_increase(initial, final): initial, final = _num("initial", initial), _num("final", final) if initial == 0: raise ValueError("initial must not be 0: the increase from zero is undefined") return (final - initial) / abs(initial) * 100def increase_by(value, percent): return _num("value", value) * (1 + _num("percent", percent) / 100)def compound_increase(percent_per_period, periods): rate, n = _num("percent_per_period", percent_per_period), _num("periods", periods) if n != n.to_integral_value() or n < 0: raise ValueError("periods must be a whole number of 0 or more") return ((1 + rate / 100) ** int(n) - 1) * 100Round only for display. In JavaScript, percentIncrease(4.5, 5.4) returns 20.000000000000007, so format it with toFixed(2). The Python version uses Decimal, which avoids that artefact, and it handles money amounts cleanly.
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.
- A starting value of 0 returns a clear message instead of a division error, because a percentage increase from zero is undefined.
- 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 increase mistakes
| Mistake | What goes wrong | What the calculator does |
|---|---|---|
| Dividing by the new value | 80 to 100 gives 20% instead of 25% | Always divides by the initial value |
| Adding percentages for repeated rises | 10% then 10% read as 20%; the true figure is 21% | Multiplies the rises and shows the combined percent |
| Undoing a rise with the same percent | A 25% rise is undone by a 20% fall, not a 25% fall | Shows the reverse percent when you ask for it |
| Mixing percent and percentage points | A rate moving from 4% to 5% called a 5% increase; it is 1 point, or 25% relative | Labels the result as relative and shows the point gap |
| Adding the percent as a number | Adding 15% to 240 as 240 + 15 = 255 instead of 276 | Converts the percent to a share of the value |
| Starting from zero | Division by zero, or a meaningless infinite percentage | Refuses with a message and shows the absolute change |
| Rounding the percent before applying it | Raising $120,000 by 5.2% rounded to 5% gives $126,000, not $126,240 | Rounds only the displayed result |
| Treating more than 100% as an error | 2,000 to 5,000 is a valid 150% increase | Accepts any positive result |
Percentage increase vs change vs difference vs percentage points
| Term | Formula | Base | Use it for |
|---|---|---|---|
| Percentage increase | (new − old) ÷ abs(old) × 100 | Starting value | A rise from a known start |
| Percentage decrease | (old − new) ÷ old × 100 | Starting value | A fall from a known start |
| Percentage change | (new − old) ÷ abs(old) × 100 | Starting value | Either direction, with a sign |
| Percentage difference | abs(a − b) ÷ ((a + b) ÷ 2) × 100 | Average of the two | Two values with no natural start |
| Percentage points | new rate − old rate | Not applicable | The gap between two percentages |
| Compound growth rate | (final ÷ initial)^(1 ÷ n) − 1 | Starting value | The steady per-period rate over n periods |
Percentage increase is the positive case of percentage change, so the two give the same number whenever the value goes up. Use the percentage change calculator when the direction is unknown, and the percentage difference calculator when neither value is the starting point, as when comparing two prices from different shops.