Inverse Variation Calculator
Solve y = k/x for y, k, or x
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Inverse Variation Calculator is built for solving y = k/x for y, k, or x — fast, free, and private. Just enter Known value 1 and Known value 2; Inverse Variation updates the result as you type. The answer from Inverse Variation arrives with its working attached. Inverse Variation replaces guesswork. Inverse Variation runs in your browser. Math data stays in the tab. Inverse Variation handles inverse variation calculator y equals k over x constant the same way as related figures — one of the Math tools on CalcProMaster. Inverse Variation is designed for real people. Labels stay plain. Inverse Variation is free, instant and local.
What the defaults give
Solving for y with 12 and 4 gives y = 3.
The tool treats the first value as k and the second as x, so 12 ÷ 4 = 3.
The formula
Solve for y: y = k ÷ x
Solve for k: k = y × x
Solve for x: x = k ÷ y
Inverse variation means the product of the two variables is fixed. If y is 12 when x is 4, then k = 48, and the pairs (1, 48), (2, 24), (4, 12), (8, 6) and (16, 3) all describe the same relationship. The input labelled "known value 1" is the numerator in modes 1 and 3, so for x you enter k first and y second.
Worked examples
y = 12 ÷ 4 → 3
k = 12 × 4 → 48
x with k = 48, y = 12 → 4
y with k = 100, x = 25 → 4
k with y = 0.5, x = 80 → 40
y with k = 60, x = 0.5 → 120
How to spot it in a word problem
The phrase that signals inverse variation is "varies inversely as" or "is inversely proportional to". If the problem says a quantity goes down as another goes up, and their product stays constant, it is inverse. Direct variation is the opposite: y = kx, and the ratio stays fixed while both grow together.
Test it with one pair before writing the equation. Multiply the two known values; if the same product turns up for every pair in the table, the relationship is inverse and that product is k. If the ratio turns up instead, it is direct.
Where it shows up physically
Boyle law is the standard example: at constant temperature, pressure times volume is constant, so compressing a gas to half its volume doubles the pressure. The same shape appears in the time taken to do a fixed amount of work — twice the workers, half the time — and in the intensity of light falling on a surface, though that one falls as the square of distance rather than directly.
Two cautions. Neither variable can be zero, because division by zero is undefined and k = y × x would give a meaningless constant. And a single data pair is not proof: fit k from one pair and check it against a second before trusting the model, since real measurements rarely sit exactly on the curve.
Frequently Asked Questions
What is inverse variation?
A relationship where the product of two variables is constant, so y = k ÷ x. Doubling one quantity halves the other.
How do I find the constant k?
Multiply the known pair: if y is 12 at x = 4, k = 48. Every other pair for that relationship multiplies to the same 48.
Which input is which in the calculator?
In the solve-for-y and solve-for-x modes, value 1 is the numerator: k in both cases. In solve-for-k mode the two values are simply y and x.
What is the difference from direct variation?
Direct variation is y = kx, where the ratio y/x stays fixed as both grow. Inverse variation fixes the product instead.
Why can neither value be zero?
Division by zero is undefined, so y = k ÷ x has no answer at x = 0. A zero also destroys the constant, since every pair would multiply to zero.
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