Free · Mathematical relations and geometry

Coordinate Gradient, Rise, Run and Distance

Calculate a line’s signed rise, run, slope, principal inclination and point-to-point distance.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

From (1, 2) to (4, 6), rise is 4, run is 3, slope is 4/3 and distance is 5. The principal line inclination is about 53.130102°.

rise=y₂−y₁; run=x₂−x₁; m=rise/run; d²=rise²+run²

Worked example

Enter these known values and leave the other values blank.

x==1==
1
y==1==
2
x==2==
4
y==2==
6
Rise
4
Run
3
Gradient
1.333
Angle
53.13 deg
Distance
5

Assumptions and limitations

  • Coordinates use the same linear scale on both axes.
  • Angle is the principal line inclination arctan(slope), not a full quadrant bearing of the directed segment.
  • A vertical line has no finite gradient. Identical points do not determine a line, though their distance is zero.
  • Coordinate and slope inverse branches need enough independent information. A positive square root can select one of two coordinate differences.

Common questions

How can I solve for a missing quantity?

Leave the unknown control empty and enter the quantities needed by the selected relation. Read the assumptions for any branch or domain restrictions.

How should I interpret the worked example?

It is an exact mathematical model with independently checked numbers. Display rounding does not change the values used for subsequent calculations.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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