Ratios Of Directed Line Segments Calculator

Ratios of Directed Line Segments Calculator

Find the point that divides a line segment internally or externally in a given ratio.

Last updated: June 2026 | By Patchworkr Team

Dividing Point

Enter both points and the ratio as real numbers.

What is the Section Formula?

For internal division, the point uses a weighted average of the endpoints.

Internal: P = (m*B + n*A) / (m + n)
External: P = (m*B - n*A) / (m - n)

Both x and y coordinates use the same ratio and the same division type.

How to Use

1. Choose internal or external division.

2. Enter the endpoints and the ratio m:n.

3. Read the live dividing point and segment lengths.

Worked Example

For internal division of A(2, 3) and B(8, 9) in ratio 2:1:

P = ((2*8 + 1*2) / 3, (2*9 + 1*3) / 3) = (6, 7)

The calculator should show (6, 7).

FAQ

Can m or n be negative?

No. This tool expects positive ratio parts.

What if m equals n in external division?

The formula becomes undefined, so the tool rejects it.

Does the same formula work for 3D?

Yes. Add the z coordinate with the same weighting.

Is the point always on the segment?

Only for internal division. External division places it outside.

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