Section Formula Calculator
Find the point dividing a line segment in a given ratio, internally or externally.
Your result will appear here as soon as you add some input.
How to use it
- 1Enter your values in the fields above.
- 2The answer and the working appear immediately below.
- 3Check the working to see the formula with your numbers substituted.
Formulas used
- Internal: P = ((m*x2 + n*x1) / (m + n), (m*y2 + n*y1) / (m + n))
- External: P = ((m*x2 - n*x1) / (m - n), (m*y2 - n*y1) / (m - n))
About the Section Formula Calculator
Internal division finds the point inside the segment that splits it in the ratio m:n measured from the first point. With m = n = 1 it reduces to the midpoint formula.
External division places the point on the extension of the line beyond one endpoint, where the distances to A and B are still in the ratio m:n but on the same side. It is undefined when m equals n, because the formula divides by (m - n).
A common use is finding the centroid of a triangle, which divides each median in the ratio 2:1 from the vertex.
Questions people ask
Is your figures uploaded to a server?
No. This tool runs entirely in your browser using standard web APIs, so your figures never leaves your device. You can confirm it by opening your browser's network panel while the tool runs, or by disconnecting from the internet after the page has loaded.
Is it free, and do I need an account?
Yes, it is free, and there is no account, no sign-up and no watermark on the result. The project is funded by optional donations.