Percentages Made Easy: Increase, Decrease and Percent Change Explained

Percentages show up everywhere: price tags, salary raises, test scores, interest rates and fitness goals. Yet many people freeze when asked to work one out. The good news is that almost every percentage problem comes down to three simple formulas. Once you know them, you can solve most everyday questions in seconds.

1. Finding a Percentage of a Number

The most basic task is finding a part of a whole.

Formula: Part = (Percent / 100) × Whole

Example: What is 15% of 80?

(15 / 100) × 80 = 0.15 × 80 = 12

A handy trick: converting the percent to a decimal (move the decimal point two places left) makes the multiplication faster.

2. Percentage Increase

Use this when a value grows, such as a price going up or a salary raise.

Formula: New Value = Original × (1 + Percent / 100)

Example: A $50 jacket rises in price by 20%.

50 × (1 + 0.20) = 50 × 1.20 = $60

3. Percentage Decrease

Use this for discounts, weight loss or falling values.

Formula: New Value = Original × (1 − Percent / 100)

Example: A $120 pair of shoes is 25% off.

120 × (1 − 0.25) = 120 × 0.75 = $90

4. Percent Change Between Two Values

Often you know the old and new values and need the percent change.

Formula: Percent Change = ((New − Old) / Old) × 100

Example: Your website traffic grew from 2,000 to 2,600 visits.

((2,600 − 2,000) / 2,000) × 100 = (600 / 2,000) × 100 = 30% increase

If the result is negative, it is a decrease. For instance, going from 2,600 back to 2,000 gives ((2,000 − 2,600) / 2,600) × 100 ≈ −23.1%.

A Common Trap

Notice that a 30% increase followed by a 23.1% decrease brings you back to the start. Increases and decreases are not symmetric, because each percentage is calculated from a different base. Likewise, a 50% drop followed by a 50% gain leaves you at 75% of the original, not 100%.

Quick JavaScript Helper

const percentOf = (pct, whole) => (pct / 100) * whole;
const increase = (value, pct) => value * (1 + pct / 100);
const decrease = (value, pct) => value * (1 - pct / 100);
const percentChange = (oldV, newV) => ((newV - oldV) / oldV) * 100;

console.log(percentChange(2000, 2600)); // 30

Wrapping Up

Remember the three building blocks: part of a whole, increase/decrease with a multiplier, and percent change relative to the original value. If you would rather skip the manual math, you can check your answers with the free online percentage and math calculators at Calcrio, which also cover finance and health calculations.

Practice with a few real numbers from your own life, and percentages will soon feel effortless.