How to Calculate Percentages: Three Formulas You'll Actually Use

Percentages show up everywhere — store discounts, tax rates, test scores, tip calculations, investment returns. Yet most people either reach for a calculator immediately or second-guess themselves halfway through the math. The good news is that you only need three formulas to handle virtually every percentage question you'll run into. Let's walk through each one with real numbers.

Formula 1: What Is X% of Y?

This is the one you'll use most often. Anytime you see "X% of" something, you're being asked to multiply.

Formula: (X ÷ 100) × Y

That's it. Divide the percentage by 100 to turn it into a decimal, then multiply by the number. Let's put it to work.

Example 1: Shopping discount

You're looking at an $85 shirt that's 20% off. How much do you save?

• (20 ÷ 100) × 85 = 0.20 × 85 = $17 off
• Sale price: $85 − $17 = $68

Example 2: Sales tax

You're buying a $250 appliance and your state charges 8.5% sales tax. What's the total?

• (8.5 ÷ 100) × 250 = 0.085 × 250 = $21.25 in tax
• Total: $250 + $21.25 = $271.25

The pattern is always the same: convert the percentage to a decimal, then multiply. Once that clicks, discounts, taxes, tips, and commissions all become the same problem with different numbers.

Formula 2: What Percent Is X of Y?

This formula answers the question "what fraction of the whole is this, expressed as a percentage?" You'll reach for it when you want to know a score, a proportion, or how big one number is relative to another.

Formula: (X ÷ Y) × 100

Divide the part by the whole, then multiply by 100.

Example 1: Test grade

You got 18 questions right out of 25. What's your percentage score?

• (18 ÷ 25) × 100 = 0.72 × 100 = 72%

Example 2: Tip calculation

You left a $45 tip on a $300 dinner bill. What percentage tip was that?

• (45 ÷ 300) × 100 = 0.15 × 100 = 15%

The key is identifying which number is the "part" and which is the "whole." The part always goes on top (numerator), and the whole goes on the bottom (denominator). If you mix them up, you'll get an answer greater than 100% for something that clearly shouldn't be — which is a good sanity check to keep in mind.

Formula 3: Percentage Change

Percentage change tells you how much something went up or down relative to where it started. You'll see it in price changes, salary bumps, weight tracking, and financial reports.

Formula: ((New Value − Old Value) ÷ Old Value) × 100

Subtract the old value from the new one, divide by the old value, then multiply by 100. A positive result means an increase; a negative result means a decrease.

Example 1: Rent increase

Your rent went from $1,400 to $1,540. What's the percentage increase?

• (($1,540 − $1,400) ÷ $1,400) × 100
• ($140 ÷ $1,400) × 100 = 0.10 × 100 = 10% increase

Example 2: Weight loss

You went from 185 lbs to 172 lbs. What's the percentage change?

• ((172 − 185) ÷ 185) × 100
• (−13 ÷ 185) × 100 = −0.0703 × 100 = −7.03%

The negative sign tells you it's a decrease — you lost about 7% of your starting weight.

Percentage Increase vs Decrease

There's no separate formula for increases and decreases — it's the same percentage change formula either way. The sign of the result tells the story:

• Positive result → percentage increase (the new value is larger)
• Negative result → percentage decrease (the new value is smaller)

So if your electricity bill went from $120 to $138, the change is ((138 − 120) ÷ 120) × 100 = +15%. If it dropped from $120 to $96, the change is ((96 − 120) ÷ 120) × 100 = −20%.

One critical detail: you always divide by the old (original) value. The starting point is your reference. If someone asks "by what percent did sales drop?" and sales went from 500 to 400, you divide by 500 — not 400. Dividing by the wrong number is one of the most common percentage mistakes people make.

Common Mistakes

Percentages are straightforward once you know the formulas, but a few traps catch people over and over again.

Dividing by the wrong number

In percentage change, you always divide by the original value — the "before" number. If a stock goes from $40 to $50, the gain is ($10 ÷ $40) × 100 = 25%. If you accidentally divide by $50 (the new value), you'd get 20%, which is wrong. The original value is always your denominator.

Confusing percentage points with percent

If an interest rate moves from 3% to 5%, that's a 2 percentage point increase — but a 66.7% percent increase ((5 − 3) ÷ 3 × 100). These sound similar but mean very different things. News headlines often blur this distinction, which is why financial reporting can feel confusing. When in doubt, ask: are they talking about the absolute difference between two percentages, or the relative change?

The reversibility trap

This one fools almost everyone at least once. If a $100 investment drops 50%, it's now worth $50. To get back to $100, you don't need a 50% gain — you need a 100% gain, because 50% of $50 is only $25. The larger the drop, the worse this asymmetry gets: a 75% loss requires a 300% gain to recover.

This is why financial advisors stress avoiding large losses. The math of recovery is brutally lopsided.

Quick Mental Math Tricks

You don't always need a calculator. These shortcuts let you estimate percentages in your head fast enough to use at a register, a restaurant, or during a conversation.

The 10% shortcut

To find 10% of any number, just move the decimal point one place to the left. 10% of $85 is $8.50. 10% of $1,400 is $140. This is your building block for everything else.

15% = 10% + half of 10%

Need to leave a 15% tip? Find 10%, then add half of that. On a $60 dinner tab: 10% is $6, half of that is $3, so 15% is $9. Quick, accurate, no phone required.

20% = 10% × 2

Double your 10% number. On a $45 bill: 10% is $4.50, so 20% is $9.00. This also works for calculating sale discounts — a 20%-off sign on a $75 item means you're saving $15 (10% is $7.50, doubled is $15).

5% = half of 10%

Once you know 10%, halving it gives you 5%. You can combine these blocks for any common percentage: 25% is 10% + 10% + 5%. On a $200 purchase: 10% is $20, so 25% is $20 + $20 + $10 = $50.

With a bit of practice, these shortcuts become second nature. You'll never need to pull out your phone to figure out a tip or sanity-check a discount again.

Last updated: March 2026