Calculate percentages, increases, decreases, and percentage differences with ease
A percentage is a number or ratio expressed as a fraction of 100. It's denoted using the percent sign (%). For example, 50% is equivalent to 50/100 or 0.5.
Percentages are used in finance for interest rates, in retail for discounts, in statistics for data analysis, and in everyday life for tips, taxes, and grades.
Basic formula: Percentage = (Part/Whole) × 100. To find a percentage of a number: Result = (Percentage/100) × Number.
To calculate percentage change: ((New Value - Old Value) / Old Value) × 100. Positive results indicate increase, negative indicate decrease.
Percentage difference compares two values: (|Value1 - Value2| / ((Value1 + Value2)/2)) × 100. Used to compare two quantities.
Percentages are crucial in finance for calculating interest rates, investment returns, inflation, discounts, markups, and tax rates.
Bill: $85.00, Tip: 18%
Tip Amount: $15.30
Total: $100.30
Original: $120, Discount: 30%
You Save: $36.00
Final Price: $84.00
Score: 85 out of 100
Percentage: 85%
Grade: B
Initial: $10,000, Final: $12,500
Gain: $2,500
Return: 25%
Purchase: $250, Tax Rate: 8.5%
Tax: $21.25
Total: $271.25
2020: 50,000, 2024: 58,000
Increase: 8,000
Growth: 16%
To find a percentage of a number, multiply the number by the percentage and divide by 100. For example, 20% of 150 = (20 × 150) ÷ 100 = 30.
Percentage change measures the change from an original value to a new value. Percentage difference compares two values without designating one as the original. Change has direction (increase/decrease), while difference is always positive.
To find the original value before a percentage was applied, divide the final value by (1 + percentage/100) for increase, or by (1 - percentage/100) for decrease. For example, if a price after 20% discount is $80, the original was $80 ÷ 0.8 = $100.
For compound percentages, apply each percentage sequentially. For example, a 10% increase followed by a 20% increase: First: 100 × 1.10 = 110, Then: 110 × 1.20 = 132, Total increase: 32%.
Percentage Increase = ((New Value - Original Value) / Original Value) × 100. If the result is negative, it's a percentage decrease. For example, from 50 to 75: ((75-50)/50) × 100 = 50% increase.
To convert a fraction to a percentage, divide the numerator by the denominator and multiply by 100. For example, 3/4 = (3 ÷ 4) × 100 = 0.75 × 100 = 75%.