What is the difference between percentage change and percentage difference?

Percentage change measures directional relative change from a specific starting baseline: ((final - initial) / |initial|) * 100. Percentage difference is non-directional and compares two values against their arithmetic mean: (|x - y| / ((x + y) / 2)) * 100.

How is Compound Annual Growth Rate (CAGR) calculated?

CAGR formula is: ((final_value / initial_value) ^ (1 / years) - 1) * 100. It computes the constant annual geometric rate of return required for an initial sum to grow to a final balance over a specified duration.

How do you calculate what percentage one number is of another?

Divide the partial amount by the total whole value, then multiply by 100: (part / total) * 100. For instance, (40 / 200) * 100 equals 20 percent.

Are my numbers or financial estimates sent to external servers?

No. All percentage arithmetic and exponential power calculations run locally in your web browser session.

Free & Private Online Browser Utility

Percentage Calculator: Increase & Discount

Solve common percentage equations, relative growth rates, and statistical proportions directly in your browser. This calculator implements six distinct calculation modes: finding X percent of Y, determining what percentage X represents of Y, computing percentage increase or decrease between two values, calculating symmetric percentage difference between two numbers, reconstructing the whole value from a percentage part, and evaluating Compound Annual Growth Rate (CAGR) over multiple periods. Each mode outputs the numerical result alongside step-by-step arithmetic derivations and mathematical formulas. Formula lines format values to 4 decimal places while derivation step totals round to 2 decimal places. Calculations evaluate client-side using floating-point math with zero server transmission.

How to use

Step 1: Select Calculation Mode

Choose between X% of Y, proportion, relative increase/decrease, percentage difference, whole value, or CAGR.
Step 2: Provide Input Numbers

Type your numeric values into the corresponding input fields.
Step 3: Examine Formulas and Steps

Review the computed percentage result and its full arithmetic derivation breakdown.

Options explained

X% of Y Mode

Computes a specified percentage fraction of a given base number using multiplication.

When to use: Use when calculating sales discounts, tips, commission rates, or tax amounts.

Percentage Increase & Decrease Mode

Calculates directional relative change between an initial baseline value and a final quantity.

When to use: Use when analyzing price fluctuations, budget growth, or performance metric shifts.

CAGR Growth Rate Mode

Evaluates Compound Annual Growth Rate over an integer number of years or compounding periods.

When to use: Use when comparing annualized financial returns, user adoption growth, or revenue milestones.

Worked example

Input: Mode: X% of Y, Percentage rate: 15%, Base value: 200

Output: Result: 30 ((15 ÷ 100) × 200 = 30)

Example calculation; proportion mode confirms 40 is 20% of 200.

Tips & limits

Percentage change requires a non-zero initial baseline number to avoid division by zero errors.
For symmetric comparisons without a clear initial baseline, use the Percentage Difference mode.
All equations evaluate in browser memory; values and inputs are never sent across the internet.

Common problems

Error: Division by zero is mathematically undefined: Ensure the denominator or baseline value is non-zero when calculating proportions or percentage change.
Negative CAGR result: CAGR requires positive starting and ending values; a negative result indicates an overall net loss.

Frequently Asked Questions (FAQ)

What is the difference between percentage change and percentage difference?: Percentage change measures directional relative change from a specific starting baseline: ((final - initial) / |initial|) * 100. Percentage difference is non-directional and compares two values against their arithmetic mean: (|x - y| / ((x + y) / 2)) * 100.
How is Compound Annual Growth Rate (CAGR) calculated?: CAGR formula is: ((final_value / initial_value) ^ (1 / years) - 1) * 100. It computes the constant annual geometric rate of return required for an initial sum to grow to a final balance over a specified duration.
How do you calculate what percentage one number is of another?: Divide the partial amount by the total whole value, then multiply by 100: (part / total) * 100. For instance, (40 / 200) * 100 equals 20 percent.
Are my numbers or financial estimates sent to external servers?: No. All percentage arithmetic and exponential power calculations run locally in your web browser session.