Calculadora de Variação Direta
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
y = k·x
About this calculator
The Direct Variation Calculator solves problems of direct proportionality between two variables, expressed by the equation y = k·x. Given two points (x1, y1) and (x2, y2) that satisfy the relationship, the tool calculates the constant of variation k = y1/x1 (or y2/x2) and optionally predicts y for a new x. It is a practical application of the linear function concept with zero intercept, useful for modeling situations where one quantity varies in the same ratio as another.
The operation is simple: enter the known x and y values from one point, and the calculator automatically determines k. If you provide a second point, it checks consistency (k must be the same). With k defined, you can estimate y for any x, or x for any y, using the formula y = k·x. The tool also displays the graph of the line y = kx, making it easy to visualize the linear relationship.
Use this calculator in everyday situations such as converting units (e.g., foreign currency to real), calculating distance traveled at constant speed, determining proportional cost (e.g., price per kg), or in physics problems like the relationship between force and elastic deformation (Hooke's Law). It is ideal for students, teachers, and professionals who need quick proportional calculations.
Cautions: ensure the relationship is truly direct variation, meaning when x doubles, y doubles in the same proportion. The calculator does not validate whether the entered data follows this condition; if the points are not proportional, the calculated k will be inconsistent. Also, avoid using x=0, as k would be undefined (division by zero). For relationships with a non-zero intercept, use a linear regression calculator.
Frequently asked questions
What does k mean in direct variation?
k is the constant of proportionality, the factor by which y is multiplied relative to x. In practice, k represents the rate of change between the quantities.
Can I use the calculator if I have only one point?
Yes, with one point the calculator finds k and allows predicting y for any x. To check if two points are proportional, enter both.
What happens if x is zero?
If x=0, the constant k is undefined (division by zero). In that case, y must also be zero for direct variation, but the calculator does not process x=0.
Does the calculator work with negative numbers?
Yes, it accepts negative values. The relationship y = k·x remains valid, and k will be negative if x and y have opposite signs.
How do I know if the relationship is direct variation?
Check if the graph of the points forms a line through the origin (0,0) and if the quotient y/x is constant. The calculator helps by confirming k is the same for all points.