BIZOMAT MAKEOS · Geometry
Distance and Angle Between Two Points
How far apart are these two points, and at what angle?
Straight-line distance in 2D and 3D, the angle in the XY plane, the slope and the midpoint between two points.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Point 1 X | mm | X of the first point. |
| Point 1 Y | mm | Y of the first point. |
| Point 1 Z | mm | Z of the first point (0 for 2D). |
| Point 2 X | mm | X of the second point. |
| Point 2 Y | mm | Y of the second point. |
| Point 2 Z | mm | Z of the second point (0 for 2D). |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Point 1 X
- What it is
- Horizontal X position of the first point, measured from the origin of the drawing, machine or coordinate system you are using.
- Units and format
- Enter a number in mm: millimetres. The form accepts -10000000 mm to 10000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Both points must use the same origin and axis directions.
What this means: Point 1 Y
- What it is
- Y position of the first point, measured from the same origin as its X value.
- Units and format
- Enter a number in mm: millimetres. The form accepts -10000000 mm to 10000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- The angle result is measured from +X towards +Y, so check which way your Y axis points.
What this means: Point 1 Z
- What it is
- Z position of the first point, the height above or below the XY plane. Leave it 0 for a flat two-dimensional problem.
- Units and format
- Enter a number in mm: millimetres. The form accepts -10000000 mm to 10000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Z changes the straight distance but not the plan distance or the angle in the XY plane.
What this means: Point 2 X
- What it is
- Horizontal X position of the second point, measured from the same origin as the first point.
- Units and format
- Enter a number in mm: millimetres. The form accepts -10000000 mm to 10000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 70 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Swapping the two points reverses the angle by 180° but leaves the distance unchanged.
What this means: Point 2 Y
- What it is
- Y position of the second point, measured from the same origin as the first point.
- Units and format
- Enter a number in mm: millimetres. The form accepts -10000000 mm to 10000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Read the value from the same datum as point 1.
What this means: Point 2 Z
- What it is
- Z position of the second point, the height above or below the XY plane. Leave it 0 for a flat two-dimensional problem.
- Units and format
- Enter a number in mm: millimetres. The form accepts -10000000 mm to 10000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the same Z datum as point 1.
Method and formulas
- Distance = √(Δx² + Δy² + Δz²); plan distance = √(Δx² + Δy²).
- Angle = atan2(Δy, Δx) from +X; slope = Δy ÷ Δx.
- Midpoint = average of the coordinates.
- Example: (10, 20) to (70, 100) is 100 mm at 53.13°.
Limitations
- Straight-line (Euclidean) distance.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check hole-to-hole distances from coordinates
- Find the angle of a line on a drawing
- Compute midpoints for layout
Who it is for
- Design engineers
- Toolmakers
- Estimators
What you get
- 3D and plan distance
- Angle in the XY plane
- Slope and midpoint
Interpreting the result
- Use the plan distance for drawings in one plane.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 40–42. Topic reference; no source tables or recommended settings are reproduced.
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