How to Calculate Percentages: Formulas & Worked Examples
To calculate X% of Y, convert the percentage into a decimal by dividing by 100, then multiply by the total: (X ÷ 100) × Y. To find the percentage change from initial to final value, subtract the initial from the final, divide by the initial, and multiply by 100: ((Final − Initial) ÷ Initial) × 100.
A percentage expresses a dimensionless ratio as a fraction of 100 (from the Latin per centum, meaning “by the hundred”). While straightforward in concept, real-world applications vary depending on whether you are calculating a simple share, growth across time, or reverse-engineering an original base before a sales tax or store discount.
1. Basic Percentage Formula
Determines the specific numerical amount representing a given fraction of a whole.
Example: What is 15% of $240?
(15 ÷ 100) × 240 = 0.15 × 240 = $36.00
2. Percentage Change / Increase / Decrease
Measures the relative change between an initial value and a subsequent final value.
Example: Revenue increased from $80k to $100k.
((100 − 80) ÷ 80) × 100 = (20 ÷ 80) × 100 = +25.0% increase
3. Ratio / Proportion Formula
Calculates what portion of a total a specific subset represents.
Example: 45 correct answers out of 180 questions on an exam.
(45 ÷ 180) × 100 = 0.25 × 100 = 25.0%
4. Reverse Percentage (Pre-Discount / Pre-Tax)
Recovers the original starting value prior to a discount or value-added tax addition.
Tax: Base = Final ÷ (1 + Tax% ÷ 100)
Example: An item costs $80 after a 20% discount.
80 ÷ (1 − 0.20) = 80 ÷ 0.80 = $100.00 original price
Excel & Google Sheets Percentage Cheat Sheet
Copy and paste these standard formulas into your spreadsheets. Remember to format the result cell using the Percentage format (`%` in the ribbon):
=(A2/100)*B2A2 = %, B2 = total=((B2-A2)/A2)A2 = start, B2 = end=A2/(1-(B2/100))A2 = final, B2 = discount %Percentage Calculation FAQs
How do you calculate percentage increase between two numbers?
Subtract the initial value from the new value, divide that difference by the original initial value, and multiply by 100. If the initial number is $50 and the new number is $75, the change is (75 − 50) ÷ 50 × 100 = 25 ÷ 50 × 100 = +50% increase.
Why is a 50% increase followed by a 50% decrease not equal to the original number?
Because the percentage base changes. If you start with $100 and increase by 50%, you reach $150. A subsequent 50% decrease is calculated against the new $150 base (50% of 150 = $75), leaving you with $75, not $100. Always keep track of the reference base.
How do I calculate pre-tax price from a total with sales tax included?
Divide the total price by (1 + tax_rate). For instance, if your receipt shows $108.00 with an 8% sales tax, calculate 108.00 ÷ 1.08 = $100.00 base pre-tax amount. Simply subtracting 8% from $108 ($108 − 8.64 = $99.36) is mathematically incorrect because the tax was levied on the lower base amount.