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Line Intersection Point Calculator

Work out line intersection point instantly with clear inputs, formula shown and shareable results.

About Line Intersection Point Calculator

Setting the two expressions for y equal gives m₁x + c₁ = m₂x + c₂, so x = (c₂ − c₁)/(m₁ − m₂). The angle between the lines comes from tan θ = |(m₁ − m₂)/(1 + m₁m₂)|.

Formulas

Intersection

x = (c₂ − c₁) / (m₁ − m₂), y = m₁x + c₁

Angle between lines

tan θ = |(m₁ − m₂) / (1 + m₁m₂)|

Worked example

With the default values below, Line Intersection Point Calculator returns Intersection point of (2, 5). Change any input above and every figure here is recalculated in your browser.

Inputs used

Gradient of the first line
2
y-intercept of the first line
1
Gradient of the second line
-1
y-intercept of the second line
7

Results

Intersection point
(2, 5)
x
2.00000000
y
5.00000000
Angle between the lines
71.565051 °

Step by step

  1. 1Values used
  2. 2Intersection
  3. 3Angle between lines
  4. 4Intersection point= (2, 5)
  5. 5x= 2.00000000
  6. 6y= 5.00000000
  7. 7Angle between the lines= 71.565051 °

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

Where do y = 2x + 1 and y = −x + 7 meet?

x = 6/3 = 2 and y = 5, so the point is (2, 5).

What does 1 + m₁m₂ = 0 mean?

The lines are perpendicular, so the angle is exactly 90° and the tangent formula would divide by zero.

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