Percentage Change Calculator
Calculate the percentage increase or decrease between two values, or find a new value after applying a percentage change. Includes direction, absolute change, and worked formula.
Last updated: March 2026
How to Use the Percentage Change Calculator
- Choose your mode — "Find % Change" if you know both values; "Find New Value" if you know the original value and the percentage change.
- Enter the original value — this is the starting number before any change occurred.
- Enter the second input — either the new value (mode 1) or the percentage change as a number, e.g., 25 for +25% or -10 for -10% (mode 2).
- Read results instantly — the primary result shows the percentage change or new value, with direction, absolute change, and the exact formula displayed below.
Understanding the Percentage Change Formula
Percentage change measures how much a quantity has changed relative to its original value, expressed as a percentage. It is one of the most commonly used calculations in business, science, finance, and everyday life. The formula is:
Percentage Change = ((New Value − Original Value) / |Original Value|) × 100
The absolute value of the original value (|Original Value|) in the denominator ensures the formula works correctly even when the original value is negative. A positive result means the value increased; a negative result means it decreased.
Percentage Increase vs Percentage Decrease
A percentage increase occurs when the new value is greater than the original (e.g., salary raised from $50,000 to $55,000: ((55,000 − 50,000) / 50,000) × 100 = +10%). A percentage decrease occurs when the new value is lower (e.g., a jacket discounted from $120 to $90: ((90 − 120) / 120) × 100 = −25%). Both use exactly the same formula; only the sign of the result differs.
Finding the New Value from a Percentage Change
If you know the original value and the percentage change, you can find the new value: New Value = Original Value × (1 + Percentage Change / 100). For a 15% increase on 200: 200 × 1.15 = 230. For a 20% decrease on 150: 150 × (1 − 0.20) = 150 × 0.80 = 120.
Why |Original Value| Is Used in the Denominator
Using the absolute value of the original ensures the sign of the percentage change correctly reflects direction regardless of whether the original value is positive or negative. For example, if a temperature changes from −10°C to −5°C, the denominator is |−10| = 10, so the change is ((−5) − (−10)) / 10 × 100 = +50%, correctly indicating an increase.
Percentage Change in Finance and Real Life
Percentage change is the language of performance measurement. Nearly every headline involving numbers — stock market reports, GDP growth, test score changes, population statistics — relies on percentage change to give context. Understanding it is one of the most practical mathematical skills.
Stock Market and Investment Returns
If you bought a stock at $45 and it is now worth $63, your percentage gain is ((63 − 45) / 45) × 100 = 40%. If it fell to $36 instead, your loss is ((36 − 45) / 45) × 100 = −20%. Investors use percentage change to compare returns across investments of different sizes — a $10 gain on a $50 investment (+20%) outperforms a $10 gain on a $200 investment (+5%).
Salary Negotiations and Pay Rises
A 5% raise on a $60,000 salary means a new salary of $60,000 × 1.05 = $63,000 — a $3,000 absolute increase. Knowing the percentage lets you compare offers across different base salaries. A 7% raise on $50,000 ($3,500 increase) is larger in absolute terms than 5% on $60,000 but represents a smaller base salary.
Percentage Points vs Percentage Change
This is one of the most misunderstood distinctions in quantitative reporting. If a party's vote share rises from 40% to 46%, that is a 6 percentage point increase — the arithmetic difference. But it is a 15% percentage change ((46−40)/40 × 100 = 15%) relative to the starting value. Journalists frequently say "6% increase" when they mean "6 percentage point increase" — these are different things with very different meanings.
Percentage Change Examples and Worked Problems
What is the percentage change from 80 to 100?
+25% increase. ((100 − 80) / 80) × 100 = (20/80) × 100 = 25%.
What is the percentage change from 100 to 80?
−20% decrease. ((80 − 100) / 100) × 100 = (−20/100) × 100 = −20%. Note: a 25% increase followed by a 20% decrease does not return to the original value because percentage changes compound.
A product costs $200. After a 30% discount, what is the sale price?
$140. New Value = 200 × (1 − 0.30) = 200 × 0.70 = $140.
A population grew from 1,200,000 to 1,350,000. What is the percentage growth?
+12.5%. ((1,350,000 − 1,200,000) / 1,200,000) × 100 = 150,000 / 1,200,000 × 100 = 12.5%.
A test score dropped from 95 to 76. What is the percentage decrease?
−20%. ((76 − 95) / 95) × 100 = (−19/95) × 100 = −20%.
If annual inflation is 4%, what does a $500 item cost next year?
$520. 500 × 1.04 = $520. The absolute price increase is $20.
How do you reverse a percentage change to find the original value?
Divide the new value by (1 + percentage change / 100). If a price is now $138 after a 15% increase: original = 138 / 1.15 = $120.
What is the percentage change from −20 to −10?
+50% increase (the value became less negative). ((−10) − (−20)) / |−20| × 100 = 10/20 × 100 = 50%.
People Also Search For
How to calculate percentage increase
Percentage Increase = ((New − Original) / Original) × 100, where New > Original. For example, from 60 to 72: ((72 − 60) / 60) × 100 = 20% increase. Only applies when the new value is larger than the original.
How to calculate percentage decrease
Percentage Decrease = ((Original − New) / Original) × 100, where Original > New. For example, from 80 to 64: ((80 − 64) / 80) × 100 = 20% decrease. This is the same formula as percentage change with the result expressed as a positive number for clarity.
What is the percentage difference between two numbers?
Percentage difference = |V1 − V2| / ((V1 + V2) / 2) × 100. Unlike percentage change, it has no "original" and "new" direction — it treats both values symmetrically. Used when comparing two independent measurements rather than before/after values.
How to calculate year-over-year percentage change
Year-over-year (YoY) change = ((This Year − Last Year) / Last Year) × 100. For example, revenue of $2.4M this year vs $2.0M last year: ((2.4 − 2.0) / 2.0) × 100 = +20% YoY growth.
How to reverse-calculate the original value before a percentage change
Original = New Value / (1 + Percentage Change / 100). If something costs $115 after a 15% increase, the original was 115 / 1.15 = $100. If something is $85 after a 15% discount, the original was 85 / 0.85 = $100.
Frequently Asked Questions
What is the percentage change formula?
Percentage Change = ((New Value − Original Value) / |Original Value|) × 100. A positive result indicates an increase; a negative result indicates a decrease.
What is the percentage change from 50 to 75?
The percentage change is +50%. Calculation: ((75 − 50) / 50) × 100 = (25 / 50) × 100 = 50%. The value increased by 50%.
How is percentage change different from percentage points?
A percentage point is the arithmetic difference between two percentages (e.g., 30% to 36% = 6 percentage points). A percentage change is the relative change: ((36 − 30) / 30) × 100 = 20%. They measure different things.
Can I enter negative numbers?
Yes. The calculator handles negative original and new values. The formula uses the absolute value of the original in the denominator, so results are correctly signed regardless of the sign of the inputs.
Why is percentage change undefined when the original is zero?
The formula requires dividing by the original value. Division by zero is mathematically undefined. If your original value is zero, percentage change cannot be computed — you can describe the absolute change instead.
Is a 50% decrease the same as halving?
Yes. A 50% decrease means the new value is 50% of the original (Original × 0.50). To reverse a 50% decrease back to the original you need a 100% increase, not a 50% increase — this asymmetry is an important property of percentage change.
How do I find the original price before a discount?
Use: Original = Sale Price / (1 − Discount%). For a $68 item after a 15% discount: 68 / (1 − 0.15) = 68 / 0.85 = $80 original price.
What is compound percentage change?
Compound percentage change applies a percentage change repeatedly. A 10% increase followed by another 10% increase is NOT a 20% increase overall. The calculation is: Original × 1.10 × 1.10 = Original × 1.21, a 21% total increase. This is why compound interest grows faster than simple interest.
Does this calculator save my data?
No. All calculations run in your browser. Nothing is sent to any server or stored after you close the page.
How do I calculate a price after VAT?
If VAT is 20%, the price after VAT = original price × (1 + 0.20) = original price × 1.20. Use "Find New Value" mode: enter the pre-VAT price as original value, enter 20 as the percentage change, and the calculator shows the post-VAT price.