A percentage increase tells you how much a value has grown relative to where it started. Whether you are comparing a salary to last year, a price tag to last month, a follower count to last quarter, or a bill to the previous billing period, the question is the same: by what percent did the number go up?
This calculator takes your original (old) value and your new value, then applies the standard percent-change formula to return the percentage rise, the raw dollar (or unit) change, and a direction code (1 = increase, −1 = decrease, 0 = no change). It works for prices, salaries, populations, test scores, and any other two-number comparison.
How to Use
- Enter the Original (Old) Value — the number you are measuring the growth from. This is the baseline, and it becomes the denominator of the formula.
- Enter the New Value — the number you are measuring the growth to. This is the figure after the change you want to evaluate.
- Set the Period (Years). Leave it at
1for a simple one-period percent change. If the change happened over multiple years (a salary over 5 years, an investment over a decade), enter that number of years — the calculator then also reports the annualized CAGR. - Read the result card. The Change Amount is the raw difference, and the Total Percentage Change line is the percent growth relative to the original value over the whole period.
- Check Annualized Growth (CAGR per Year) when the period is longer than one year. This spreads the total growth evenly across each year, which is the fair way to compare multi-year performance.
- Read the Direction code:
1means the value grew,−1means it shrank, and0means there was no change. - If the original value is 0, percent change is mathematically undefined; the calculator safely returns 0% instead of an Infinity or NaN, so you always get a stable number rather than an error.
The math updates instantly as you type, so you can tab between the two fields and watch the percent respond to even a one-unit change.
The Percentage Increase Formula
The formula used by this calculator is the textbook percent-change formula taught in middle-school pre-algebra and used by every financial analyst:
Percentage Increase = (New Value − Original Value) ÷ Original Value × 100
In plain steps:
- Step 1 — Find the change amount. Subtract the original value from the new value:
new − original. A positive result means growth; a negative result means a decline. - Step 2 — Divide by the original value. This measures the change relative to where you started, which is why the original number is the denominator and not the new one. Dividing by the new value instead would give the wrong answer.
- Step 3 — Multiply by 100. Converts the ratio into a percentage.
Worked example: going from 50 to 75. The change amount is 75 − 50 = 25. Divide by the original, 25 ÷ 50 = 0.5. Multiply by 100 = +50%. A jump from 50 to 75 is a 50% increase, which matches the result card.
Compare that with going from 100 to 150: the change amount is 50, but 50 ÷ 100 = 0.5 = also +50%. The raw dollar change is the same 50, but because the baseline was double, the percentage is identical — which is exactly why percentages, not raw differences, are the fair way to compare growth across different starting sizes.
Annualized Growth (CAGR)
When a change unfolds over multiple years, the total percentage change overstates the yearly experience, because compounding does the heavy lifting. The Compound Annual Growth Rate (CAGR) spreads the total growth evenly across each year:
CAGR = ((New ÷ Original)^(1 ÷ Years) − 1) × 100
For example, $100 growing to $200 over 5 years is a 100% total gain, but the CAGR is ((200 ÷ 100)^(1/5) − 1) × 100 ≈ 14.87% per year. That is the equivalent steady yearly growth that would turn $100 into $200 after five compounded years. Set Period (Years) to 1 and the CAGR equals the total percentage change — they are the same number for a one-year span.
Why the Denominator Matters
A common mistake is to divide the change by the new value instead of the original. On a price that rose from $80 to $100, the correct increase is (100 − 80) ÷ 80 = 20 ÷ 80 = 25%. Dividing by 100 instead would give 20%, understating the rise. Always anchor the percentage to the number you started from.
The same logic in reverse produces a percentage decrease. Going from $200 to $150 gives (150 − 200) ÷ 200 = −50 ÷ 200 = −25%. The negative sign is the tool's way of telling you the value shrank. Note that going down 25% and then up 25% does not bring you back to the start: $200 → $150 (−25%) → $187.50 (+25% on 150). This asymmetry is why percentage changes are not reversible by simply applying the opposite percent.
Examples
Example 1 — A raise at work. Your salary moved from $50,000 to $60,000. The change amount is $10,000, and the percentage increase is (60,000 − 50,000) ÷ 50,000 × 100 = 10,000 ÷ 50,000 × 100 = +20%. A 20% raise means your paycheck grew by one-fifth of its original size.
Example 2 — A price hike. Groceries rose from $120 to $150 over the year. The change is $30, and 30 ÷ 120 × 100 = +25%. Your grocery bill now costs a quarter more than it did, which is a more useful number than the raw $30 because it lets you compare it against a salary increase of, say, 3% — the 25% grocery rise is outpacing your income.
Example 3 — A six-figure move. A startup's monthly recurring revenue grew from $1,000,000 to $1,250,000. The change amount is $250,000, but the percentage increase is 250,000 ÷ 1,000,000 × 100 = +25%, the same percent as the grocery example despite the numbers being 8,000 times larger. The engine handles magnitudes of a million or more with no rounding surprises.
Example 4 — When the value falls. Stock went from $200 to $150. (150 − 200) ÷ 200 × 100 = −25%. The direction code is −1, marking this as a decrease even though you typed the same two fields in the same order — the sign carries the direction.
Example 5 — A 5-year investment. An investment grew from $10,000 to $20,000 over 5 years. The total percentage change is +100%, but set Period (Years) = 5 and the annualized CAGR is about 14.87% per year — the smooth yearly return that doubles the money over half a decade.
FAQ
What is the percentage increase formula?
Percentage increase = (New Value − Original Value) ÷ Original Value × 100. First subtract the original from the new to get the change, then divide that change by the original value, and finally multiply by 100 to turn the ratio into a percentage. If the result is negative, the value actually decreased.
How do I calculate a 50 to 75 increase?
Going from 50 to 75, the change is 75 − 50 = 25. Divide 25 by the original 50 to get 0.5, then multiply by 100 for a 50% increase. The new value is one-and-a-half times the original.
What is the difference between percentage increase and percentage change?
They use the exact same formula: (new − old) ÷ old × 100. "Percentage increase" is the positive-direction framing — the result is reported as growth. "Percentage change" is the neutral version that can come out positive or negative. When the new number is smaller, this calculator simply reports a negative percentage increase (a decrease).
Why does dividing by zero give an error?
The original value is the denominator. If it is 0, there is no baseline to measure growth against — any change off zero is mathematically undefined, not "infinite percent." The calculator flags this as an error instead of returning a misleading number. To measure growth off zero, describe it as an absolute amount, not a percentage.
Can I use this calculator for prices, salaries, and test scores?
Yes. The formula is unit-agnostic: it works on dollars, people, pounds, points, or followers as long as both numbers use the same units. Enter the two figures in the same currency or scale and the percentage increase is identical regardless of what the numbers represent.
Why is a 20% decrease followed by a 20% increase not back to the start?
Percentages are anchored to whatever value they are applied to. Drop $100 by 20% to $80, then add 20% of $80 (which is $16) and you land at $96, not $100. The second 20% is a smaller dollar amount because it is calculated on the smaller $80 base. This asymmetry is normal and is why you cannot reverse a percent change by applying the opposite percent to the result.
What is the difference between total percentage change and CAGR?
Total percentage change is the whole story over the entire period. CAGR (Compound Annual Growth Rate) spreads that same total growth evenly across each year, as if it compounded at a steady rate. If a $10,000 investment doubles to $20,000 in 5 years, the total change is +100% but the CAGR is about 14.87% per year. Use CAGR to compare growth across different time spans; use total change to describe the full move.
Disclaimer
This percentage increase calculator is provided for informational purposes only and does not constitute financial, mathematical, or tax advice. Results are based on the exact values you enter and the standard percent-change formula; rounding, compounding, and real-world context can alter how the figure should be interpreted. Always verify important calculations independently before making a financial decision.