Distance from Point to Plane Calculator

Compute the perpendicular distance from a 3D point (x, y, z) to a plane ax + by + cz + d = 0, plus the signed distance and the foot of the perpendicular.

Frequently Asked Questions

What is the formula for distance from a point to a plane?

The absolute value of a x naught plus b y naught plus c z naught plus d, divided by the square root of a squared plus b squared plus c squared. The denominator is the length of the normal vector.

Signed versus unsigned distance?

The signed distance keeps the sign, telling you which side of the plane the point lies on (positive if it lies on the side the normal points to). The unsigned distance is its absolute value.

How do I find the closest point on the plane?

Start from the point and move along the negative of the unit normal by the signed distance. The result is the foot of the perpendicular.

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Estimates for informational purposes only.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.

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