How to use the proportion calculator
Pick a relationship type first. Equivalent ratios is the classic A/B = C/D. Direct proportion and Inverse proportion relabel the boxes as two (x, y) pairs. Then fill in three values and leave the one you want blank. It can be any of the four.
Each box takes a whole number, a decimal, a fraction like 3/4, or scientific notation like 1.2e3. The answer comes back as an exact fraction first, then as a decimal rounded to the precision you pick.
- Choose Equivalent ratios, Direct proportion or Inverse proportion.
- Label the quantities for yourself so matching ones sit in matching boxes.
- Type three values and leave exactly one box blank. Fill all four to run a check instead.
- Press Solve proportion.
- Read the exact answer, then confirm the two cross products match.
Solve proportions with cross multiplication
Two ratios are equal exactly when their cross products are equal. So A/B = C/D becomes A x D = B x C, an ordinary equation you can solve for whichever letter is missing. That's all a cross multiplication calculator does, and this one works with the blank in any position.
For 3/4 = 9/D, cross multiplying gives 3D = 36, so D = 12. For A/6 = 5/9, you get 9A = 30, so A = 10/3. The calculator keeps 10/3 as the answer and shows 3.333333 separately, so a rounded decimal never replaces the exact value.
A / B = C / D means A x D = B x C (B and D can't be 0)Missing A = (B x C) / DMissing B = (A x D) / CMissing C = (A x D) / BMissing D = (B x C) / A
Setting up a word problem
Most wrong answers come from the setup, not the arithmetic. Keep the same kind of quantity in both top boxes and the same kind in both bottom boxes. If A is dollars, C is dollars. If B is items, D is items.
Put both sides in the same units, too. A map scale written in centimeters per kilometer has to stay centimeters over kilometers on both sides.
| Problem | Top boxes (A and C) | Bottom boxes (B and D) | Example |
|---|---|---|---|
| Price for a quantity | Cost | Number of items | $6/2 = $15/5 |
| Map scale | Map distance | Real distance | 2 cm/5 km = 8 cm/20 km |
| Similar shapes | Side on shape 1 | Matching side on shape 2 | 3/5 = 9/15 |
| Percent | Part | Whole | 18/60 = 30/100 |
| Recipe | Ingredient amount | Batches | 2 cups/1 batch = 6 cups/3 batches |
Checking whether two ratios are proportional
Fill in all four boxes and the calculator becomes a proportion checker. It multiplies across both ways and says Proportional only if the two products match exactly. For 4/9 and 12/27, both products are 108, so they're equal. For 4/9 and 12/28, you get 112 and 108, so they aren't.
When the values come from measurements, an exact match is rare. The calculator shows how far apart the products are, but it won't decide for you how close counts as close enough. That depends on how precise the measurements were.
Direct and inverse proportion
In a direct proportion, both values grow together and their ratio stays fixed: y = kx. If 3 notebooks cost $7.50, the constant k is $2.50 per notebook, so 8 notebooks cost $20. Direct mode shows k for both pairs so you can see they match.
In an inverse proportion, one goes up as the other goes down and their product stays fixed: y = k / x. A job of 240 worker-hours takes 6 people 40 hours, or 10 people 24 hours, because 6 x 40 and 10 x 24 both equal 240. Inverse mode checks the products instead of the cross products.
Real life bends both rules. A delivery fee breaks a direct price model, and adding workers stops cutting time once they get in each other's way. Use the model only while one constant holds.
Direct: y = kx, so y1 / x1 = y2 / x2Inverse: y = k / x, so x1 x y1 = x2 x y2
| x | Direct y = 2.5x | Inverse y = 240 / x |
|---|---|---|
| 3 | 7.5 | 80 |
| 6 | 15 | 40 |
| 8 | 20 | 30 |
| 10 | 25 | 24 |
| 12 | 30 | 20 |
Worked proportion examples
Each row shows the equation the calculator builds and the check it runs on the answer.
| Mode and input | Equation | Answer | Check |
|---|---|---|---|
| Equivalent: 3/4 = 9/D | 3D = 4 x 9 | D = 12 | 3 x 12 = 4 x 9 = 36 |
| Equivalent: A/6 = 5/9 | 9A = 30 | A = 10/3 | 9 x 10/3 = 30 |
| Check: 4/9 and 12/27 | 4 x 27 vs 9 x 12 | Proportional | 108 = 108 |
| Check: 4/9 and 12/28 | 4 x 28 vs 9 x 12 | Not proportional | 112 vs 108 |
| Direct: (3, 7.5) and (8, y) | y / 8 = 7.5 / 3 | y = 20 | Both constants are 2.5 |
| Inverse: (6, 40) and (10, y) | 6 x 40 = 10y | y = 24 | Both products are 240 |
Zeros, fractions and decimals
B and D can't be zero in A/B = C/D, because you can't divide by zero. A top value can be zero, but it can leave the missing value with no answer or with infinitely many. The calculator tells you which instead of guessing.
Decimals are taken exactly as typed. 0.75 becomes 3/4, but 0.33 means 33/100, not one third. If you mean a third, type 1/3.
Sources
These references cover cross products, proportion word problems and direct and inverse variation.