Length Of A Line Segment
Calculate the straight-line distance between two endpoints on a 2D coordinate grid using the Euclidean distance formula. Free segment length calculator for geometry students and teachers with step-by-step results.
Point A (x₁, y₁)
Point B (x₂, y₂)
About This Calculator
The Length Of A Line Segment Calculator computes the straight-line distance (length) between two endpoints on a 2D coordinate plane. Whether you are a geometry student learning the distance formula, a teacher preparing classroom examples, or a professional needing quick coordinate measurements, this tool provides instant and accurate results.
How the Formula Works
The calculator uses the Euclidean distance formula d = √((x2 − x1)² + (y2 − y1)²), derived from the Pythagorean theorem. A line segment connecting two points forms the hypotenuse of a right triangle whose legs are the horizontal difference |x2 − x1| and the vertical difference |y2 − y1|. Applying the Pythagorean theorem a² + b² = c² to these legs gives the segment length c.
Applications of Line Segment Length
Measuring line segment lengths is fundamental in coordinate geometry, computer graphics (rendering line segments and paths), navigation (straight-line distances), engineering (blueprint measurements), and physics (displacement vectors). In analytic geometry, segment length calculations appear in problems involving triangles, circles, polygons, and vector magnitudes.
How to Use the Calculator
Enter the X and Y coordinates for Point A (x₁, y₁) and Point B (x₂, y₂) in their respective fields. The calculator supports decimal numbers, negative values, and integers. Once all four coordinates are entered, click "Calculate Length" to instantly see the segment length with up to 4 decimal places. Use the share button to copy your calculation to the clipboard.
Frequently Asked Questions
What is the formula for the length of a line segment?
The length of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is given by the Euclidean distance formula: d = √((x₂ - x₁)² + (y₂ - y₁)²). This formula is derived from the Pythagorean theorem and calculates the straight-line distance between the two points.
How do I find the length of a line segment with endpoints?
Subtract the x-coordinates (x₂ - x₁) and square the result. Subtract the y-coordinates (y₂ - y₁) and square the result. Add both squared values together, then take the square root. This gives you the straight-line length of the segment.
What is the difference between a line and a line segment?
A line extends infinitely in both directions and has no endpoints, while a line segment is a finite portion of a line with two distinct endpoints and a fixed measurable length. A line is denoted with arrows on both ends, whereas a line segment uses a bar notation AB̅.
Can I calculate the length of a 3D line segment with this calculator?
This calculator is designed for 2D coordinates (x, y). For 3D line segments (x, y, z), the formula extends to d = √((x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²). Check our 3D distance calculator on Calculy for three-dimensional measurements.
What is the length of the line segment from (0,0) to (3,4)?
Using the formula d = √((3-0)² + (4-0)²) = √(9 + 16) = √25 = 5 units. This is a classic 3-4-5 Pythagorean triple example.
Does the calculator work with negative coordinates?
Yes, the calculator works with both positive and negative coordinate values. The distance formula squares the differences, so it correctly handles any combination of positive or negative real numbers for all four coordinates.
Is this tool free to use?
Yes, all calculators on Calculy are completely free to use. No registration, login, or payment is required. You can also share your calculation results via the share button.