Section Formula Calculator

Work out section formula instantly with clear inputs, formula shown and shareable results.

About Section Formula Calculator

The internal section formula gives the point dividing a segment in the ratio m : n as ((m·x₂ + n·x₁)/(m + n), (m·y₂ + n·y₁)/(m + n)). Note the weights are swapped relative to the points.

Formula

Section formula

P = ((m·x₂ + n·x₁)/(m + n), (m·y₂ + n·y₁)/(m + n))

Worked example

With the default values below, Section Formula Calculator returns Dividing point of (3.5, 5). Change any input above and every figure here is recalculated in your browser.

Inputs used

First point (x, y): 2, 3
Second point (x, y): 8, 11
Ratio part mminimum 0: 1
Ratio part nminimum 0: 3

Results

Dividing point: (3.5, 5)
x coordinate: 3.50000000
y coordinate: 5.00000000
Distance from the first point: 2.50000000

Step by step

1Values used
2Section formula
3Dividing point= (3.5, 5)
4x coordinate= 3.50000000
5y coordinate= 5.00000000
6Distance from the first point= 2.50000000

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Divide (2,3) to (8,11) in the ratio 1 : 3.

((8 + 6)/4, (11 + 9)/4) = (3.5, 5), a quarter of the way along.

Why are the weights swapped?

Because a point closer to the first point corresponds to a small m, so the first point must carry the larger weight n.