Calculator Tools

Distance and Midpoint Calculator

Find the distance and midpoint between two points in 2D or 3D. Step-by-step distance formula, midpoint formula, Manhattan, and Chebyshev distance.

Dimension

Choose 2D for the standard distance and midpoint formulas, or 3D for points in space (x, y, z).

Decimal places

Point P

Accepts integers, decimals (1.5), and simple fractions (3/4).

Point Q

Accepts integers, decimals (1.5), and simple fractions (3/4).

Quick examples

Result

Between (1, 2) and (4, 6)

Distance d

Euclidean (straight-line) distance in 2D

Midpoint M

Average of the coordinates

(2.5, 4)

Manhattan distance

Sum of absolute differences (taxicab, L1)

Chebyshev distance

Largest absolute difference (chessboard, L∞)

Direction vector q − p

Componentwise difference

(3, 4)

Vector magnitude

Length of q − p (equals the Euclidean distance)

Slope m

(y₂ − y₁) / (x₂ − x₁)

1.333333

Angle of inclination

atan2(Δy, Δx)

53.1301°

Point PPoint QMidpoint M

Distance derivation

1.d = √( (x₂ − x₁)² + (y₂ − y₁)² )
2.d = √( (3)² + (4)² )
3.d = √( 9 + 16 )
4.d = √ 25
5.d = 5

Midpoint derivation

1.M = ( (x₁ + x₂)/2, (y₁ + y₂)/2 )
2.M = ( (1 + 4)/2, (2 + 6)/2 )
3.M = (2.5, 4)

Formulas used

Distance formula (Euclidean)

2D: d = √((x₂ − x₁)² + (y₂ − y₁)²)
3D: d = √((x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)²)
Manhattan: |Δx| + |Δy| (+ |Δz| in 3D)
Chebyshev: max(|Δx|, |Δy| [, |Δz|])

Midpoint formula

2D: M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
3D: M = ((x₁ + x₂)/2, (y₁ + y₂)/2, (z₁ + z₂)/2)
Slope (2D only): m = Δy / Δx
Angle (2D only): θ = atan2(Δy, Δx)

How to use

Pick a dimension. Choose 2D for the standard x and y coordinates, or 3D to add a z axis for points in space.
Type the components of Point P and Point Q. The fields accept integers, decimals, signed numbers, and simple fractions like 3/4.
Read the Distance d (Euclidean), the Midpoint M, plus Manhattan distance, Chebyshev distance, and the direction vector. In 2D the tool also reports slope and angle of inclination.
Open the Distance derivation and Midpoint derivation lists to see the step-by-step substitution and arithmetic the way a textbook would write it out.
Tap Copy on any result card to copy a single value, or Copy summary to grab the full report with both derivations as plain text.
Use the Quick examples to load classic textbook points (origin to (3, 4), the unit cube diagonal, fractional coordinates) or tap Swap P and Q to flip the points.

About this tool

Distance and Midpoint Calculator finds the straight-line (Euclidean) distance and the midpoint between two points in either the 2D plane or in 3D space, using the standard textbook formulas. In 2D it applies d = sqrt((x2 - x1)^2 + (y2 - y1)^2) and M = ((x1 + x2)/2, (y1 + y2)/2). In 3D it adds the z component to both. Along with the main result, the tool also reports the Manhattan (L1, taxicab) distance, the Chebyshev (L-infinity, chessboard) distance, the direction vector q - p with its magnitude, and (in 2D only) the slope and angle of inclination of the line through the two points. Each output card has its own Copy button, and a Copy summary button copies a plain-text report with the step-by-step derivation, so you can paste it directly into a homework write-up or a lab notebook. Inputs accept integers, decimals, signed numbers, European comma-decimals, and simple fractions like 3/4 or -7/8 so you can solve textbook problems without first converting them. A coordinate-plane SVG preview draws Point P, Point Q, the line segment between them, and the midpoint marker so you can sanity-check the math at a glance. Everything runs in your browser; coordinates and results are never uploaded.

Free to use. Works in your browser. No signup, no login.

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