How to Use Inverse Proportion Calculator
The Inverse Proportion Calculator makes it easy to find an unknown in any inverse relationship without manual algebra.
- Choose what to solve for — Select "Solve for y₂" or "Solve for x₂" using the toggle at the top of the Inverse Proportion Calculator.
- Enter the known pair — Fill in x₁ and y₁. These two values establish the constant of proportionality k.
- Enter the second known value — Provide either x₂ (when solving for y₂) or y₂ (when solving for x₂).
- Read the result — The Inverse Proportion Calculator instantly displays the unknown value along with the full substitution working.
The Inverse Proportion Calculator also shows the constant k and the step-by-step derivation beneath the result, helping you understand where the answer comes from.
Formula & Theory — Inverse Proportion Calculator
The Inverse Proportion Calculator is based on the inverse proportionality law:
y = k / x where k = x₁ × y₁
Because the product is constant for all corresponding pairs:
x₁ × y₁ = x₂ × y₂
This means:
y₂ = (x₁ × y₁) / x₂
x₂ = (x₁ × y₁) / y₂
| Symbol | Meaning |
|---|---|
| x₁, y₁ | A known pair of inversely proportional values |
| x₂, y₂ | A second pair, one of which is unknown |
| k | Constant of proportionality (k = x₁ × y₁) |
When x doubles, y halves — that is the core property the Inverse Proportion Calculator relies on.
Domain Restriction
Neither x nor y can be zero in an inverse proportion, because division by zero is undefined. The Inverse Proportion Calculator will not compute a result if any denominator is zero.
Use Cases for Inverse Proportion Calculator
The Inverse Proportion Calculator is useful whenever two quantities vary inversely:
- Speed and time — If a journey at 60 km/h takes 4 hours, the Inverse Proportion Calculator finds how long the same journey takes at 80 km/h.
- Workers and days — If 5 workers finish a job in 12 days, find how many days 8 workers need using the Inverse Proportion Calculator.
- Unit price and quantity — Given a fixed budget, find how many items you can buy as price changes.
- Gear ratios — Calculate output speed from input speed when gear teeth counts are known.
- Pressure and volume — Apply Boyle's Law (P₁V₁ = P₂V₂) directly with the Inverse Proportion Calculator.
- Math homework — Verify inverse proportion exercises step by step with the full working shown.
Wherever one quantity increases while another decreases proportionally, the Inverse Proportion Calculator delivers the answer with transparent working.