The Complete Guide to Percentage Calculations: Increase, Decrease & Reverse
Master percentage formulas for shopping discounts, salary raises, profit margins, and reversing sales tax.
Understanding the Core Concept of Percent
The word percent comes from the Latin per centum, meaning “by the hundred.” Every percentage is simply a fraction with a denominator of 100. Converting a percentage to a decimal is as simple as moving the decimal point two places to the left: 25% becomes 0.25, and 7.5% becomes 0.075.
1. Calculating Percentage Increase and Growth
When measuring growth—such as an investment portfolio gain, a population change, or an annual salary increase—you find the difference between the new value and the initial value, then divide by the original value.
If your hourly wage increases from $20.00 to $23.50, what was your percentage raise?
1. Find the dollar difference: $23.50 − $20.00 = $3.50.
2. Divide by the initial wage: $3.50 ÷ $20.00 = 0.175.
3. Multiply by 100: 0.175 × 100 = 17.5% raise.
2. Calculating Percentage Decrease and Discounts
Discounts on retail items and reductions in energy usage represent percentage decrease. The formula is identical in structure to increase, but the difference reflects reduction from the original price.
A winter coat costs $120.00 and is discounted by 30%. What is the checkout price?
1. Multiply $120.00 by 0.30 to find the discount amount: $36.00.
2. Subtract discount from original price: $120.00 − $36.00 = $84.00 final price.
Quick shortcut: Multiply $120.00 directly by (1 − 0.30 = 0.70) = $84.00.
3. Reverse Percentages (Finding the Original Pre-Tax Value)
A common mistake when removing 20% VAT or sales tax is subtracting 20% from the final bill. That is mathematically incorrect because the tax was calculated on the pre-tax base, not the final total. To reverse a percentage, divide by (1 + rate).
A computer receipt shows $1,150.00 including a 15% sales tax. What was the pre-tax price?
Divide the final amount by 1.15: $1,150.00 ÷ 1.15 = $1,000.00 pre-tax price.
Notice that subtracting 15% from $1,150 ($172.50) would give $977.50, which is incorrect!