Rule of three calculator
If 3 workers finish a job in 8 days, how long do 6 workers take? If 2 kg of flour makes 12 rolls, how much flour for 30 rolls? Enter three known values and get the fourth using direct or inverse proportion. Essential for recipes, unit pricing, and quick estimates.
Enter any three values — the fourth will be calculated.
A
B
C
Result
X = 15
How to solve a proportion
1. Identify whether the relationship is direct (more → more) or inverse (more → less).
2. Enter the three known values in the labeled fields.
3. Read the computed fourth value.
4. Sanity-check: does the answer scale in the right direction?
Proportion examples
Direct proportion — recipe scaling
2 cups sugar → 24 cookies; 5 cups sugar → ? cookies. Direct: (5 ÷ 2) × 24 = 60 cookies.
Inverse proportion — workers and days
4 workers → 12 days; 6 workers → ? days. Inverse: (4 × 12) ÷ 6 = 8 days.
Unit price comparison
$7.50 for 500 g; how much for 1.2 kg? Direct: (7.50 ÷ 500) × 1200 = $18.00.
When to use the rule of three
• When you scale ingredient lists or chemical mixtures by mass or volume.
• When you estimate project duration from known team-size tradeoffs (rough inverse models).
• When you convert quantities at a fixed ratio without reopening a spreadsheet.
When to choose something else
• When the relationship is not linear — e.g. compound interest or physics formulas with squares.
• When you need proper dimensional analysis across unit systems — use dedicated converters.
• When bulk discounts change unit price — proportion assumes a constant rate.
Direct vs inverse in everyday problems
Direct: maps at 1:50,000 scale — double map distance means double real distance. Inverse: fixed pool volume — wider pipe (more flow) means less time to fill. Misclassifying direct as inverse is the most common student error; ask "if I double the first quantity, does the second double or halve?"
Limits of the rule of three
It assumes constant proportionality. Paint coverage drops on porous walls; network speed is not strictly proportional to user count; food cooking time does not scale linearly with portion size. Use proportion for first-order estimates, then validate with experience or specs.
Frequently asked questions
What is direct proportion?
When one quantity increases, the other increases at a constant ratio. Example: more miles at the same speed means more time.
What is inverse proportion?
When one increases, the other decreases so their product stays constant. Example: more workers often means fewer days for the same job.
What is the cross-multiply formula?
Direct: a/b = c/x → x = (b × c) ÷ a. Inverse: a × b = c × x → x = (a × b) ÷ c.
Can I use this for currency exchange?
Yes at a fixed rate. Real markets fluctuate — refresh the rate for large transfers.
Why did my worker-days answer look wrong?
Real projects are not perfectly inverse — communication overhead and indivisible tasks break the simple model.
Is data uploaded?
No. Calculations run locally in your browser.