Distance From a Point to a Line Calculator

Find the Shortest Distance from a Point to a Line

Calculate the perpendicular distance from a point to a line using the formula \(d = \frac{|ax_0 + by_0 + c|}{\sqrt{a^2 + b^2}}\). Complete step-by-step solution shown for every calculation.
Distance Formula

For a line in general form:

\[ ax + by + c = 0 \]

and a point \(P(x_0, y_0)\), the shortest distance is:

\[ d = \frac{|ax_0 + by_0 + c|}{\sqrt{a^2 + b^2}} \]
Enter Line Coefficients
Enter Point Coordinates
Distance \(d\)
—
Enter coefficients and click "Calculate Distance"
📐 Step-by-step solution will appear here after calculation.
Note: The distance formula calculates the perpendicular (shortest) distance from the point to the line. If the point lies exactly on the line, the distance is 0.

More References and Links

  • General Equation of a Line: \(ax + by + c = 0\)
  • Math Calculators and Solvers
  • Geometry Calculators and Solvers