Length Of A Line Segment Calculator - Distance, Midpoint, Slope

The length of a line segment is the straight-line distance between its two endpoints, which makes it the most fundamental measurement you can take on a segment in analytic geometry.

• • Coordinate geometry homework: Verify the distance between two plotted points, including the 3-4-5 and 5-12-13 right triangles that show up constantly in textbooks.
• • CAD, mapping, and design layouts: Quickly check the linear distance between two reference points in 2D drawings or full 3D models before cutting or placing parts.
• • Physics and engineering problems: Compute displacement between an initial position and a final position when the path is a single straight segment.
• • Game development and computer graphics: Measure the distance between two game objects, vertices in a 3D mesh, or waypoints in a navigation graph.

A line segment is the portion of a line bounded by two distinct endpoints, so it always has a finite, non-negative length equal to the Euclidean distance between them. Leave the z values at 0 for a 2D problem, or enter nonzero z1 and z2 for a 3D segment, and the result updates as you type.

When the segment is the chord of a circle, Chord Length Calculator applies the same distance formula between two points on the circumference.

The calculator applies the Euclidean distance formula to the two endpoints you enter. For a 2D segment between (x1, y1) and (x2, y2), the length is the square root of the sum of squared coordinate differences; a 3D segment adds a third squared term for the z difference.

• x1, y1, z1: Coordinates of the first endpoint. Use the same unit system throughout (meters, feet, centimeters, or unitless coordinates).
• x2, y2, z2: Coordinates of the second endpoint. Leave z1 and z2 at 0 for a 2D problem so the third term drops out.
• L: Length of the line segment, returned in the same unit system as the coordinates.

Squaring the differences removes any sign, so negative coordinates work the same as positive ones, and the square root of a non-negative sum is always non-negative.

According to Wolfram MathWorld, the Euclidean distance between two points is d = sqrt((x2 - x1)^2 + (y2 - y1)^2) in 2D and extends to 3D as d = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2).

According to Wikipedia, the Euclidean distance between two points in the plane equals the length of the line segment connecting them and is computed from the square root of the sum of squared coordinate differences.

To check the integer legs of a right triangle, Pythagorean Triples Calculator lists every classic triple, including 3-4-5 and 5-12-13, that the length of a line segment formula evaluates to exactly.

Four small ideas show up every time you measure a line segment. Understanding them keeps the calculator output honest.

These four concepts map directly onto the calculator outputs, so each one shows up as a labeled row in the results panel.

When the segment is one side of a right triangle, Right Triangle Calculator fills in the remaining sides, angles, and area from the same two-endpoint input style.

Using the calculator is a four-step flow. Open the page, type the endpoint coordinates, and read the results on the right.

1. 1 Enter the first endpoint: Type the x and y (and z, for 3D) coordinates of the first endpoint. The defaults (0, 0, 0) are a useful starting point for an origin-based segment.
2. 2 Enter the second endpoint: Type the x and y (and z, for 3D) coordinates of the second endpoint. The defaults (5, 12, 0) form a 5-12-13 right triangle so you can confirm the formula immediately.
3. 3 Read the length of the line segment: The Euclidean distance appears at the top of the results panel and updates as you type. The page reports 4 decimal places for sub-unit accuracy and 2 for larger values.
4. 4 Check the midpoint and slope: The midpoint triple and the xy-plane slope appear below the length. Use the slope to classify the segment as horizontal (0), vertical (undefined), or sloped.
5. 5 Switch to 3D if needed: Type nonzero z1 and z2 to extend the formula to 3D. The length grows by the square root of the squared z difference, the midpoint triple now includes a z value, and the slope row keeps the xy-plane projection.
6. 6 Reset and try another segment: Press Reset to restore the default endpoints, which is the fastest way to compare several line segments side by side.

Suppose you are measuring a wall that runs from (0, 0) to (3, 4) on a floor plan measured in meters. Type 0 and 0 for the first endpoint, then 3 and 4 for the second. The length of the line segment reads 5 m, the midpoint is (1.5, 2), and the slope of the wall is 4/3.

These benefits come from real measurement, drafting, and study tasks rather than treating the tool as a generic math toy.

• • Two endpoints in, full geometry out: Returns length, midpoint, and slope at once, so one form fill replaces three separate computations.
• • Works in 2D and 3D without switching tools: Leave z1 and z2 at 0 for a 2D problem, then enter nonzero z values for a 3D segment. The same formula generalizes through the z-axis term.
• • Catches vertical segments explicitly: The xy-plane slope row reports 'undefined' for vertical segments instead of producing a divide-by-zero error, so the length and midpoint still display correctly.
• • Slope stays interpretable in 3D: For 3D segments the xy-plane slope is still useful for the projected view, while the full 3D direction comes from the (dx, dy, dz) triple.
• • Real-time updates as you type: Every change to an endpoint refreshes the results in real time, which is useful for sensitivity checks.
• • Accepts negative coordinates: Origin-crossing or negative coordinates work the same as positive ones because the squared differences remove any sign, keeping textbook problems and CAD coordinates on equal footing.
• • Pairs with related geometry tools: The same math powers the chord length, arc length, slope, and Pythagorean solvers here, so you can switch tools without re-entering values.

The biggest practical benefit is that the length of a line segment becomes a single reading instead of a multi-step calculation, and the value can be copied straight into a worksheet or fixture specification.

When the length of a line segment is one side of a triangle, Triangle Calculator fills in the remaining sides, angles, and area from the same coordinate inputs.

These factors determine whether the calculator's result matches the value you need on a drawing, in a model, or on paper.

• • The calculator assumes a flat Euclidean plane or space. On a curved surface such as a sphere, the length of a line segment must be computed along a great circle and will not match the Euclidean value.
• • The result reflects the straight-line distance between the endpoints, not the path length along a curve. For piecewise or curved paths, integrate or sum the segment lengths individually.

Treat the length of a line segment as an exact analytic value whenever the endpoints are coordinates in a flat space. For geographic, geodetic, or curved-surface problems, use a distance-on-sphere tool instead, since the chord on a sphere is always shorter than the surface arc.

According to Wikipedia, a line segment is the part of a line bounded by two distinct endpoints, so it always has a finite, non-negative length that can be measured directly between those two endpoints.

If the endpoint coordinates need to be in a different unit system or reference frame, Coordinates Converter translates the numbers before the segment length is computed.