Choose the percentage problem you need to solve, enter your values, and view the precise mathematical result with full algebraic step-by-step explanations.
Quick Presets:
1. What is X% of Y?
%
Percentage Result
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📝 Step-by-Step Mathematical Solution:
PROPORTION VISUALIZER:0%
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Standard Percent: (X / 100) × Y
Percentage Change: ((New − Old) / Old) × 100
Discount Formula: Original × (1 − %/100)
Reverse Percent: Final / (1 ± %/100)
Understanding percentages
A percentage is a dimensionless ratio expressed as a fraction of 100 (from the Latin per centum meaning "by the hundred"). Saying 20% of $85 means taking 20 parts out of 100 equal parts of $85, giving $17.00. Percentages allow standard comparisons across different baselines.
Percentage change explained
Percentage change measures relative growth or reduction compared to the initial baseline: % Change = ((New Value − Initial Value) / Initial Value) × 100.
A positive percentage indicates an increase (growth/markup), whereas a negative percentage represents a decrease (decline/discount). Notice that a 50% increase followed by a 50% decrease does not return to the starting number (e.g. 100 + 50% = 150; 150 − 50% = 75).
Frequently asked questions
How do I calculate a percentage of a number?▶
Multiply the number by the percentage divided by 100. For example 20% of 250 = 250 × 20/100 = 50.
How do I calculate percentage change?▶
Use the formula (New - Old) / Old × 100. From 50 to 65 that is (65 - 50)/50 × 100 = +30% increase.
What percent is 25 of 200?▶
Divide 25 by 200 and multiply by 100: (25 / 200) × 100 = 12.5%.
How does reverse percentage work?▶
If an item costs $120 after a 20% discount, the original price was $120 / (1 - 0.20) = $150.