Section Formula Calculator: Internal and External Division
Enter points A and B and the ratio m : n. Choose internal or external division and get the point P with the working.
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Point P
(7, 3)
- Distance AP
- 6.7082
- Distance PB
- 2.2361
P lies between A and B, with AP : PB = m : n.
Show working
- P = ((m·x₂ + n·x₁) / (m + n), (m·y₂ + n·y₁) / (m + n))
- x = (3 × 8 + 1 × 4) / 4 = 7
- y = (3 × 5 + 1 × −3) / 4 = 3
How to use
- Choose internal or external division.
- Enter A(x₁, y₁), B(x₂, y₂) and the ratio m : n.
- Read the point P and the steps.
Good to know
Internal division: P = ((m·x₂ + n·x₁)/(m + n), (m·y₂ + n·y₁)/(m + n)). This is the section formula from NCERT Class 10 "Coordinate Geometry". For example, (4, −3) and (8, 5) divided 3 : 1 gives (7, 3).
External division puts P outside AB on the line extended: P = ((m·x₂ − n·x₁)/(m − n), (m·y₂ − n·y₁)/(m − n)). It is not possible when m = n. (External division is mainly a Class 11–12 and competitive-exam topic.)
The ratio m : n is AP : PB. A ratio of 1 : 1 gives the midpoint. To find the ratio in which a given point divides AB, write the ratio as k : 1 and solve for k.
Questions
What is the section formula?
For internal division in m : n, P = ((m·x₂ + n·x₁)/(m + n), (m·y₂ + n·y₁)/(m + n)).
What is the difference between internal and external division?
Internal division puts P between A and B; external division puts P on the line beyond A or B.
Which point gets m: A or B?
m multiplies the coordinates of B and n those of A, because AP : PB = m : n.
How do I find the points of trisection?
Use ratios 1 : 2 and 2 : 1. Those two points divide AB into three equal parts.
Is anything I enter stored?
No. The calculation runs in your browser and nothing is sent to a server.