Calculate compound growth and decline over time

What This Calculator Does

The compound percentage calculator calculates the final value after repeated percentage growth or decline over multiple periods. Unlike simple percentage multiplication, compound calculations use exponential formulas because each period's change builds on the previous result.

Compound Growth Formula

Final = Start × (1 + Rate ÷ 100)^periods

Compound Decline Formula

Final = Start × (1 − Rate ÷ 100)^periods

The exponent (number of periods) is what makes compounding exponential rather than linear. This matters enormously for investments, business growth, inflation analysis, and long-term projections.

For single-period percentage changes, use our percentage change calculator instead.

How Compound Formulas Work

Let's break down the compound growth formula step-by-step with a concrete example:

Example: $1,000 growing at 5% for 3 periods

Formula Breakdown

Final = Start × (1 + Rate ÷ 100)^periods

$1,000 × (1 + 5 ÷ 100)³

$1,000 × (1.05)³

$1,000 × 1.157625

$1,157.63

Why Each Period Compounds

Period 1: $1,000 × 1.05 = $1,050

Period 2: $1,050 × 1.05 = $1,102.50 (not $1,100!)

Period 3: $1,102.50 × 1.05 = $1,157.63

Notice how each period multiplies the previous result, not the original value. This creates exponential growth that accelerates over time.

For a comprehensive explanation with more examples, read our guide on compound growth rate explained with examples.

Compound vs. Simple Percentage Change

The most common mistake is confusing compound percentages with simple multiplication. Here's the critical difference:

Simple (WRONG for compound scenarios)

"10% growth for 3 periods = 30% total growth"

$1,000 × 1.30 = $1,300

Compound (CORRECT)

"10% growth for 3 periods = 33.1% total growth"

$1,000 × (1.10)³ = $1,000 × 1.331 = $1,331

Difference: $31 or 3.1 percentage points

The difference seems small in this example, but over longer periods or higher rates, the divergence becomes enormous. After 20 periods at 10%, simple multiplication gives you 200% growth, but compound growth gives you 572.75%!

For single-period increase or decrease calculations without compounding, use our increase and decrease calculator.

Compound Decline and Loss Scenarios

Compounding works both ways—repeated losses compound downward using the decline formula:

Final = Start × (1 − Rate ÷ 100)^periods

Example: $100,000 declining 5% annually for 5 years

$100,000 × (1 − 5 ÷ 100)⁵

$100,000 × (0.95)⁵

$100,000 × 0.773781

$77,378.09

Notice this is not $75,000 (which would be a simple 25% decline). Compound decline is actually less severe than simple multiplication suggests because each period's loss is applied to a smaller base.

However, compounding still accelerates losses compared to linear decline. Understanding this helps with budget planning, depreciation analysis, and risk assessment.

For detailed scenarios and examples, read our article on compound decline and repeated loss scenarios.

Common Applications

Compound percentage calculations appear in many real-world contexts:

Finance and Investing

Investment returns: Calculate portfolio growth over years with compound annual returns. Example: $10,000 at 7% for 20 years = $38,696.84

Inflation: Project purchasing power decline. Example: $50,000 salary losing 2% purchasing power annually for 10 years = $40,877.30 real value

Loan growth: Calculate debt growth with compound interest (though loans often use different compounding rules)

Business and Marketing

Revenue growth: Model revenue scenarios. Example: $100,000 monthly revenue growing 5% per month for 12 months = $179,585.63

User base growth: Project customer or subscriber growth rates

Churn and retention: Calculate impact of customer loss over time

Science and Demographics

Population growth: Model population changes with birth/death rates

Decay rates: Calculate radioactive decay or depreciation

Learn more applications in our compound growth rate explained guide.

Learn More and Related Tools

Compound percentage calculations connect to other percentage workflows:

Related Calculators:

• Percentage Change Calculator - Single-period percentage changes
• Increase and Decrease Calculator - Apply simple percentage increases/decreases
• Percent of Number Calculator - Understand individual period calculations

Educational Resources:

Explore our compound growth guides for detailed tutorials on exponential growth, investment projections, and business forecasting. All calculations run client-side—your data stays private. Free to use, no signup required, available in 12 languages.