Distance Calculator

Calculated using standard mathematical and industry formulas.

Calculate exact Euclidean distance between two points in 2D or 3D Cartesian coordinates, midpoint, line slope, and speed-distance-time physics problems.

How to use this calculator?

1. For coordinate distance: enter x₁, y₁, x₂, y₂ and get the Euclidean distance, midpoint, and slope.
2. For 3D distance: switch to '3D Coordinates' and add z₁, z₂.
3. For Speed-Distance-Time: select which variable to solve for and enter the other two.

Formula & calculation method

Euclidean Distance & Speed-Distance-Time Formulas

d = √((x₂−x₁)² + (y₂−y₁)²) · Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2) · Speed = Distance / Time

In 3D, add (z₂-z₁)² under the square root. Speed × Time = Distance.

Step-by-step calculation example

Points (0, 0) and (3, 4): d = √(9 + 16) = 5. Midpoint = (1.5, 2). Slope = 4/3 ≈ 1.33.

Key insights to remember

• The Euclidean distance formula d = √((x₂-x₁)² + (y₂-y₁)²) is the 2D form of the Pythagorean theorem.
• In 3D: d = √((Δx)² + (Δy)² + (Δz)²) — commonly used in physics, 3D graphics, and GPS calculations.
• Speed = Distance / Time is the backbone of kinematics — consistent units are essential.
• The midpoint formula gives the exact centre of a line segment: ((x₁+x₂)/2, (y₁+y₂)/2).

How to interpret your results?

Slope

Slope m = Δy / Δx gives the rate of rise per unit of horizontal run. A slope of 0 is horizontal; an undefined slope is vertical.

Midpoint

The midpoint divides the segment exactly in half — useful for bisecting lines in geometry and finding centre coordinates in mapping.

Frequently asked questions

What is Euclidean distance?

Euclidean distance is the straight-line distance between two points in Euclidean space using the Pythagorean theorem.

How do you calculate 3D coordinate distance?

Add the z-coordinate squared difference under the square root: d = √((Δx)² + (Δy)² + (Δz)²).

What is the midpoint formula?

The midpoint M is the average of coordinates: M = ((x₁+x₂)/2, (y₁+y₂)/2).

How do you calculate line slope?

Slope m is vertical rise divided by horizontal run: m = (y₂ - y₁) / (x₂ - x₁).

How do you calculate distance from speed and time?

Use the physics formula Distance = Speed × Time with consistent units.

What is the difference between Euclidean and Manhattan distance?

Euclidean distance measures straight-line distance, while Manhattan distance measures grid-based distance (|Δx| + |Δy|).

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