About the Line Intersection Calculator
Two straight lines on a flat plane either cross at one point, never meet because they are parallel, or lie on top of each other. Enter two points on each line and this calculator finds which case applies. When the lines cross it gives the exact point, and it also writes each line as an equation of the form ax + by = c. Type two points on line 1 and two points on line 2 and the line intersection appears at once, with a few related figures underneath, and you can copy the result with one tap. The sums run in your browser, so nothing you enter is uploaded.
Updated October 2026
How to use the Line Intersection Calculator
- 1Enter two points on line 1 and two points on line 2.
- 2Pick the units or options from the menus if the line intersection tool offers them.
- 3Read the line intersection in the large result box.
- 4Look at the extra rows for related figures.
- 5Press Copy result to keep the answer.
When you need the line intersection
Students check graph problems with it, and builders, designers and programmers use it to find where two edges or paths meet in a plan or a game.
The lines in this tool are infinite, so the crossing point can lie outside the segments you typed. If you need to know whether two line segments meet, check that the crossing point lies between the end points on both.
How the line intersection is worked out
Each line becomes A·x + B·y = C, where A = y₂ − y₁, B = x₁ − x₂ and C = A·x₁ + B·y₁. The crossing point is x = (C₁B₂ − C₂B₁) ÷ D and y = (A₁C₂ − A₂C₁) ÷ D, with D = A₁B₂ − A₂B₁. The line through (0, 0) and (4, 4) and the line through (0, 4) and (4, 0) cross at (2, 2). A line through (0, 0) and (1, 2) is parallel to one through (0, 1) and (1, 3), so D = 0.
Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.
- Both line equations shown
- Detects parallel and identical lines
- Exact crossing point
Mistakes to avoid with line intersection
Make sure that the two points on a line are different, or no line exists. When D is exactly 0 the lines are parallel or the same, and no single crossing point exists. Rounded decimals can hide an exactly parallel pair.
On phone and computer
On a phone, type into the boxes one after another and read the line intersection underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the line intersection move. The line intersection calculator works the same on both.
Checking your line intersection by hand
A good habit is to test the line intersection calculator with a case you already know. The line through (0, 0) and (4, 4) and the line through (0, 4) and (4, 0) cross at (2, 2). A line through (0, 0) and (1, 2) is parallel to one through (0, 1) and (1, 3), so D = 0.
If your own figures give a surprising answer, repeat the working yourself: Each line becomes A·x + B·y = C, where A = y₂ − y₁, B = x₁ − x₂ and C = A·x₁ + B·y₁. The crossing point is x = (C₁B₂ − C₂B₁) ÷ D and y = (A₁C₂ − A₂C₁) ÷ D, with D = A₁B₂ − A₂B₁. Small differences usually come from rounding, from mixing units, or from a typing slip in one of the inputs. Finding where lines meet is easier when each line is clear. Find a line's steepness with the Slope Calculator, the distance between points with the Distance Calculator, and how far a point is from a line with the Point to Line Distance Calculator.
Features
- The lines are infinite, not segments
- Two different points per line
- D = 0 means parallel or same
- Clear messages when the line intersection inputs make no sense
- Copy the result with one tap
- Private: nothing is uploaded
Frequently asked questions
How do I calculate line intersection?
Each line becomes A·x + B·y = C, where A = y₂ − y₁, B = x₁ − x₂ and C = A·x₁ + B·y₁. The crossing point is x = (C₁B₂ − C₂B₁) ÷ D and y = (A₁C₂ − A₂C₁) ÷ D, with D = A₁B₂ − A₂B₁. The line through (0, 0) and (4, 4) and the line through (0, 4) and (4, 0) cross at (2, 2). A line through (0, 0) and (1, 2) is parallel to one through (0, 1) and (1, 3), so D = 0.
What is the formula for line intersection?
Each line becomes A·x + B·y = C, where A = y₂ − y₁, B = x₁ − x₂ and C = A·x₁ + B·y₁. The crossing point is x = (C₁B₂ − C₂B₁) ÷ D and y = (A₁C₂ − A₂C₁) ÷ D, with D = A₁B₂ − A₂B₁. The line intersection calculator applies it exactly and rounds only the displayed answer to six significant figures.
How do you know if lines are parallel?
Their slopes are equal, which is the same as D = 0 in the formula.
What if the lines are the same?
Then every point is shared, so there is no single intersection point.
Can lines cross outside my points?
Yes, because the lines go on forever past the points you entered.
Is this line intersection calculator free and private?
Yes. It is free, needs no account and runs in your browser, so the numbers you type are not uploaded or stored.