ConverterHub

Direct Variation Calculator

Find the constant k in y = kx and predict a new y value.

How it is calculated

For a relationship y = k × x the tool first finds the constant from your known pair, k = known_y / known_x, then predicts y = k × new_x. Both results are shown with four decimals. The known x cannot be zero, because k would need a division by zero, so that case returns no result. A known y of zero is accepted and gives k = 0, which means every prediction is 0. Negative values are accepted too and simply give a negative k. The tool works in one direction only: it predicts y from a new x; to go from a y back to an x, swap which quantity you enter as x and y. Units are your choice, but the new x must use the same unit as the known x.

Worked example

Suppose 8 metres of fabric cost 28, and you want the price of 13 metres. Step 1: k = 28 / 8 = 3.5 per metre. Step 2: y = 3.5 × 13 = 45.5. The tool prints a constant k of 3.5000 and a predicted y of 45.5000. The line passes through the origin, so zero metres would cost zero.

Try this example →

Common mistakes

  • Using direct variation for data that has a fixed starting amount, such as a delivery fee plus a price per item. Those follow y = kx + b, and the prediction here would be wrong.
  • Putting the known x and y in the wrong boxes. Swapping them gives the inverse constant and a wrong forecast.
  • Mixing units between the known pair and the new x, for example kilograms in the pair and grams in the new value.
  • Entering 0 as the known x. A pair with x = 0 cannot define k, so choose another known pair.

About this calculator

Two quantities are in direct variation when their relationship can be written as y = kx, meaning y grows in exact proportion to x through a fixed constant k, so doubling x always doubles y. Given one known pair of x and y values, the constant of variation is found by isolating k = y / x, and once k is known it predicts y for any new value of x (and, by rearranging to x = y / k, x for any new value of y).

This is one of the first proportional-relationship models taught in algebra, and it describes many real-world quantities: distance traveled at constant speed equals speed times time, the cost of buying items at a fixed unit price equals price times quantity, and currency conversion at a fixed exchange rate all follow the same y = kx pattern.

Enter a known x and y pair to find the constant k, then enter a new x value and this calculator predicts the corresponding y using that same proportional relationship. To go the other way and find x from a new y, divide y by the k it shows.

Was this helpful?

You can pick up to 3 reactions.

Comments

  • Be the first to comment.

Popular calculators

Loan Calculator

Monthly payment, total interest and full amortization schedule.

Percentage Calculator

Percent change, percent of, and ratio calculations.

Discount Calculator

Calculate final price, savings, and discount amount.

BMI Calculator

Body mass index from height and weight (metric or imperial).

Age Calculator

Compute your exact age in years, months and days from a birth date.

Compound Interest Calculator

Calculate the final amount and interest earned with compounding.

All Calculators