Plane Equation & Point-to-Plane Distance Calculator
Plane Equation & Distance Calculator in Oxyz Ax + By + Cz + D = 0
Write a plane equation or find the distance from a point to a plane. Each step states the formula first, then substitutes the numbers you entered.
The calculator above writes the equation of a plane from a point and a normal vector (or three points) and computes the distance from a point to the plane.
Formulas used
A(x − x₀) + B(y − y₀) + C(z − z₀) = 0
d = |Ax + By + Cz + D| / √(A² + B² + C²)
- n = (A; B; C) is the normal vector of the plane.
Worked example
Distance from M(1; 2; 3) to x + 2y + 2z − 2 = 0:
d = 9/3 = 3
Enter the same values in the calculator above to see every step of the solution.
How to use the calculator
- Enter a point and a normal vector, or three points, and the point for the distance.
- Press the calculate button. The result appears instantly.
- Read the step-by-step solution, rendered with KaTeX, to check your own work.