Calculators
Section Formula Calculator
Find the Cartesian point dividing a line segment in a positive ratio using the internal section formula, privately in your browser.
Divide a line segment in a chosen ratio.
For endpoints A(x₁, y₁) and B(x₂, y₂), a point P dividing the segment in the ratio AP:PB = m:n has coordinates ((n x₁ + m x₂)/(m+n), (n y₁ + m y₂)/(m+n)). The fraction of the way from A to B is m/(m+n). For A = (0, 0), B = (6, 8), and ratio 1:2, P = (2, 8/3), one third of the way from A to B. Equal ratio parts give the midpoint. Positive ratio parts locate P inside the segment; external division and zero ratio parts are not supported. Identical endpoints return that same point for every positive ratio. Use a flat Cartesian plane with consistent units, not latitude and longitude. Signed decimal coordinates and scientific notation are accepted. Coordinate magnitudes must be zero or 1e-100 to 1e100, and each ratio part must be 1e-100 to 1e100. Results use browser floating-point arithmetic with up to 12 significant digits; extreme ratios and tiny differences between large coordinates may round to an endpoint. Inputs remain in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
Which way does the ratio work?
The ratio is AP:PB = m:n. A ratio of 1:2 places P one third of the way from A toward B. The coefficient of B is m/(m+n).
How do I find the midpoint?
Use equal positive ratio parts, such as 1:1 or 5:5. The result is the average of the two x coordinates and the average of the two y coordinates.
Does this support external division?
No. Both ratio parts must be positive, so the result divides the segment internally. Zero and negative ratio parts are rejected.
What happens with identical endpoints?
The division point is the same as both endpoints for any accepted positive ratio.
What are the limits and precision?
Use zero or coordinate magnitudes from 1e-100 to 1e100 and ratio parts from 1e-100 to 1e100. Results are approximate and display up to 12 significant digits. Extreme ratios may round to an endpoint. This is a flat Cartesian calculation, not a geographic one.
Are my inputs uploaded?
No. Coordinates and ratios are processed entirely in your browser.