Percentage Calculator

About the Percentage Calculator

Percentages come up everywhere — discounts, tips, tax rates, investment returns, grade calculations, growth rates. Three problems trip people up most: what is X% of Y, what percent is X of Y, and what's the percent change from X to Y. This page covers all three with formulas and worked examples.

The Formula

What is X% of Y? Answer = (X ÷ 100) × Y. What percent is A of B? Answer = (A ÷ B) × 100. Percent change from old to new? Answer = ((new − old) ÷ old) × 100.

Worked Example

What is 15% of 200? (15 ÷ 100) × 200 = 30. What percent is 45 of 180? (45 ÷ 180) × 100 = 25%. Percent change from 80 to 100? ((100 − 80) ÷ 80) × 100 = 25% increase. Percent change from 100 to 80? ((80 − 100) ÷ 100) × 100 = −20% (a decrease of 20%).

Percent increase vs percent decrease — and why they are not symmetric

If a stock falls 50%, it does not need to rise 50% to recover — it needs to rise 100%. This asymmetry catches investors off guard. A $100 stock that drops to $50 has fallen 50%; to get back to $100 it must rise by $50, which is 100% of the new value of $50. The base of the percentage matters.

Percentage points vs percent

If interest rates rise from 4% to 5%, that is a 1 percentage point increase but a 25% increase in the rate itself. Financial news mixes these up all the time. Use 'percentage points' (pp) when comparing two percentages, and 'percent' when describing relative change.

Compound percentages: when applying percentages in sequence

Applying a 10% discount then a 10% tax is not the same as zero net change. $100 × 0.90 × 1.10 = $99 — the order matters less than the fact you are taking percentages of different bases. The result is always slightly less than the simple sum suggests.

Common Mistakes

• Confusing 'X% more' with 'X% of'. 'Sales rose 200%' means they tripled (200% MORE than before, so 100% + 200% = 300% of original). 'Sales are 200% of last year' means they doubled.
• Subtracting percentages from different bases. A 50% drop followed by a 50% rise does not return you to the start.
• Using the wrong base for percent change. The change is always divided by the old value, not the new one.

Frequently Asked Questions

How do I calculate a discount?
Discount amount = Original × (Discount% ÷ 100). Final price = Original − Discount, or equivalently Original × (1 − Discount% ÷ 100). A 25% off $80 item: $80 × 0.75 = $60.

How do I add a tip or sales tax?
Final = Original × (1 + Rate% ÷ 100). $50 bill with 18% tip: $50 × 1.18 = $59.

What's the difference between simple and compound percent growth?
Simple growth adds the same dollar amount each period. Compound growth applies the percentage to the most recent value, so the dollar growth itself grows. See our compound interest calculator for the long-term effect.

This calculator is for informational purposes only and does not constitute financial, tax, or legal advice. Consult a licensed professional before making significant financial decisions.