Percentage Change Calculator

How is percentage change calculated? Step-by-step

Percentage change measures how much a value has grown or shrunk relative to its starting point. The formula: See also: the Percentage Calculator and the Discount Calculator.

Percentage Change = ((New − Old) ÷ |Old|) × 100

Worked example — increase: Sales grew from ₹80,000 to ₹1,00,000. Change = (1,00,000 − 80,000) ÷ 80,000 × 100 = 20,000 ÷ 80,000 × 100 = +25%.

Worked example — decrease: Temperature dropped from 40°C to 32°C. Change = (32 − 40) ÷ 40 × 100 = −8 ÷ 40 × 100 = −20%.

Percentage change vs percentage difference

These are two different calculations with different meanings. Percentage change is directional — it compares a new value to an old "reference" value. Percentage difference is non-directional — it compares two values without implying one came before the other. Formula: Percentage Difference = |V₁ − V₂| ÷ ((V₁ + V₂) ÷ 2) × 100. Example: comparing 80 and 100: percentage difference = |80−100| ÷ ((80+100)÷2) × 100 = 20 ÷ 90 × 100 = 22.2%.

Real-world percentage change examples

Percentage change with negative numbers

When the old value is negative, the formula still works but direction can be counterintuitive. From −50 to −25: (−25−(−50)) ÷ |−50| × 100 = 25 ÷ 50 × 100 = +50% (increased in value, less negative). From −50 to −100: (−100−(−50)) ÷ |−50| × 100 = −50 ÷ 50 × 100 = −100% (decreased, more negative). When the old value is 0, percentage change is undefined — division by zero.

Frequently asked questions about percentage change

Is a 200% increase the same as tripling?

Yes. A 100% increase doubles a value. A 200% increase triples it. Starting from 100: +100% = 200; +200% = 300. The formula: New = Old × (1 + % change / 100). At 200% increase: 100 × 3 = 300.

How do you reverse a percentage change?

To find the original value after a percentage change: Old = New ÷ (1 + % change / 100). If a price increased 25% to ₹500: Old = 500 ÷ 1.25 = ₹400. Note: reversing a 20% discount is NOT subtracting 20% from the discounted price — it requires dividing by 0.8.

What is CAGR and how does it relate to percentage change?

CAGR (Compound Annual Growth Rate) is the annualised percentage change over multiple years. Formula: CAGR = (End Value ÷ Start Value)^(1/years) − 1 × 100. An investment growing from ₹1 lakh to ₹1.61 lakh in 5 years: total change = +61%. CAGR = (1.61)^(1/5) − 1 = 10% per year. Related: Percentage Calculator · Investment Calculator · ROI Calculator

Percentage change in finance and investing

Stock return and portfolio percentage change

Percentage change is the foundational metric for measuring investment returns. If a stock bought at ₹500 is now ₹650: percentage change = (650−500)/500 × 100 = +30%. This is identical to the "absolute return" shown in mutual fund statements. Key distinction: absolute return (percentage change) ignores time. CAGR adjusts for duration. Example: +30% over 1 year (CAGR = 30%) vs +30% over 5 years (CAGR = 5.39%) — same percentage change, very different performance.

Inflation: purchasing power percentage change

Inflation measures the percentage change in the price level (CPI) year over year. India's CPI (Consumer Price Index) changed from 161.3 in May 2023 to 178.2 in May 2026 (hypothetical). Percentage change = (178.2−161.3)/161.3 × 100 = +10.5% over 3 years, CAGR = 3.38%/year. Purchasing power change: if inflation = 6%/year, ₹100 today is worth (100 × (1−0.06)³) = ₹83.06 in 3 years — a −16.9% purchasing power change. Track your salary raises against CPI: if your salary grew 12% but inflation was 15%, your real purchasing power decreased by approximately 2.6%.

Population and census: interpreting percentage change

Rapid urbanisation means percentage changes in Indian metro populations often exceed 50–100% over 10 years. Related: Percentage Calculator · ROI Calculator · Inflation Calculator

Sources: WHO Expert Consultation 2004; ICMR Guidelines; standard mathematical references.

Compounding vs simple percentage change over multiple periods

A common mistake: adding percentage changes. If a stock rises 50% then falls 50%, it does not return to the original value. Rise 50%: ₹100 → ₹150. Fall 50%: ₹150 → ₹75. Net result: −25%, not 0%. The correct method for compounding: multiply (1 + r₁) × (1 + r₂) × ... × (1 + rₙ) and subtract 1. Rise 50% + fall 50%: 1.5 × 0.5 = 0.75 → −25% net change. Always use the compounding formula for multi-period returns in investing and business analysis.

Sources: CFA Institute Investment Foundations; SEBI Investor Education materials; RBI Financial Literacy resources.

Percentage change vs percentage difference: which to use?

Percentage change is directional — it compares a new value to a specific original (reference) value. Use when measuring growth, decline, or movement: salary increase, stock return, inflation rate, weight loss progress.

Percentage difference is non-directional — it compares two values without implying one came "before" the other. Formula: |V₁ − V₂| ÷ ((V₁ + V₂) ÷ 2) × 100. Use when comparing two items of equal status: price of product A vs product B, test score of student A vs student B.

Common use cases: real-world percentage change examples

Related: Percentage Calculator (X% of Y, reverse percentage) · ROI Calculator (investment return) · Inflation Calculator (purchasing power change)

Related calculators

How is this different from the Percentage Calculator?

This page is specifically for the difference between two values — percentage increase, decrease, and growth rates. For the broader part-whole questions (what is 25% of 800, 200 is what % of 800, reverse percentages), use the general percentage calculator.