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Calculate part-to-whole relationships, percentages, and proportions
Formula:
Percentage = (Part ÷ Whole) × 100
Enter values to calculate part-to-whole relationship
Part-to-whole relationships describe how a portion (part) relates to the complete amount (whole). This fundamental concept is used throughout mathematics, statistics, and everyday life. It can be expressed as a percentage, ratio, fraction, or decimal.
Percentage = (Part ÷ Whole) × 100
Example: (25 ÷ 100) × 100 = 25%
Part = (Percentage ÷ 100) × Whole
Example: (25 ÷ 100) × 100 = 25
Whole = (Part ÷ Percentage) × 100
Example: (25 ÷ 25) × 100 = 100
Decimal = Part ÷ Whole
Example: 25 ÷ 100 = 0.25
Ratio = Part : Whole
Example: 25:100 or simplified 1:4
Fraction = Part/Whole
Example: 25/100 or simplified 1/4
| Part | Whole | Percentage | Ratio | Decimal |
|---|---|---|---|---|
| 25 | 100 | 25% | 1:4 | 0.25 |
| 50 | 100 | 50% | 1:2 | 0.50 |
| 75 | 100 | 75% | 3:4 | 0.75 |
| 15 | 60 | 25% | 1:4 | 0.25 |
| 30 | 40 | 75% | 3:4 | 0.75 |
| 18 | 20 | 90% | 9:10 | 0.90 |
A part-to-whole relationship describes how a portion (part) relates to the complete amount (whole). For example, if you scored 18 out of 20 on a test, 18 is the part and 20 is the whole. This can be expressed as a percentage (90%), ratio (18:20 or 9:10), fraction (18/20 or 9/10), or decimal (0.90).
Divide the part by the whole, then multiply by 100. Formula: Percentage = (Part ÷ Whole) × 100. For example, if 30 students out of 50 passed, the percentage is (30 ÷ 50) × 100 = 60%. This means 30 is 60% of 50.
Multiply the whole by the percentage, then divide by 100. Formula: Part = (Percentage ÷ 100) × Whole. For example, to find 25% of 80: Part = (25 ÷ 100) × 80 = 0.25 × 80 = 20. So 25% of 80 is 20.
Divide the part by the percentage, then multiply by 100. Formula: Whole = (Part ÷ Percentage) × 100. For example, if 15 is 30% of the whole: Whole = (15 ÷ 30) × 100 = 0.5 × 100 = 50. So 15 is 30% of 50.
Part-to-whole compares a portion to the total (e.g., 3 out of 10 = 3:10), while part-to-part compares different portions to each other (e.g., 3 boys and 7 girls = 3:7 boys to girls). Part-to-whole always includes the complete total, while part-to-part compares components without referencing the total.
To convert percentage to decimal: divide by 100 (25% = 0.25). To convert decimal to percentage: multiply by 100 (0.25 = 25%). To convert to fraction: use percentage as numerator over 100 (25% = 25/100 = 1/4). To convert fraction to percentage: divide numerator by denominator, then multiply by 100 (1/4 = 0.25 = 25%).