Distance Between Two Lines

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Calculate the shortest distance between two parallel lines in 2D space.

Line Equation (Ax + By + C = 0)

Coefficient A

Coefficient B

Constant C₁ (Line 1)

Constant C₂ (Line 2)

Identified Lines

L₁: 3x + 4y + 5 = 0

L₂: 3x + 4y + 15 = 0

Distance Result

Distance (d)

Common Magnitude5.00

Offset Shift10

InterpretationThese lines are definitively parallel.

About this calculator

Measuring Between Lines

The distance between two parallel lines is the constant perpendicular distance between any point on one line and the other line. If the lines are not parallel, the distance is zero (they intersect), unless they are skew lines in 3D space. This calculator focuses on the 2D parallel case.

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Pro Tips

To use this formula, both lines must be written in the form Ax + By + C = 0 with the same A and B values.
If the coefficients are different, normalize them (e.g., if one is 2x+4y and the other is x+2y, multiply the second by 2).
If the lines are identical, the distance is zero.

Fun Facts

"Parallel lines never meet in Euclidean geometry, but in projective geometry, they meet at the 'point at infinity'."
"This calculation is essential in CNC machining to ensure proper tool offset distances."
"Architects use parallel line distancing to define corridor widths and structural spacing."

Formula: d = |C₂ - C₁| / √(A² + B²)