Survey Join and Radiate Calculator: Bearing and Distance Between Points, or a Point from a Bearing and Distance

Bearings and distances for surveyors and students.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose join or radiate.

Enter the eastings and northings, or the bearing and distance.

The calculator gives the bearing and distance, or the new coordinates.

Formulas used

  • \theta = \operatorname{atan2}(\Delta E, \Delta N)
  • d = \sqrt{\Delta E^2 + \Delta N^2}
  • E_2 = E_1 + d\sin\theta,\ N_2 = N_1 + d\cos\theta

Worked example

With the default numbers in the calculator above:

  1. Bearing from the first point to the second, in decimal degrees: 33.690068 degrees
  2. Bearing in degrees minutes seconds: 33 deg 41 min 24.24 sec
  3. Bearing in quadrant form: N 33 deg 41 min 24.24 sec E
  4. Horizontal distance: 180.277564 m
  5. Change in easting: 100 m
  6. Change in northing: 150 m
  7. Reverse bearing (second point back to the first): 213 deg 41 min 24.24 sec

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want to do? Radiate: new point from a bearing and distance; Bearing (for a radiation), clockwise from north 225 deg; Distance (for a radiation) 100 m.

  1. Easting of the new point: 929.289322 m
  2. Northing of the new point: 929.289322 m
  3. Bearing used, in degrees minutes seconds: 225 deg 0 min 0.00 sec

Common questions

How is a bearing measured?

Clockwise from north, from 0 to 360 degrees. A quadrant bearing is given as an angle from north or south toward east or west.

How do I find the bearing between two coordinates?

Take the arctangent of the change in easting divided by the change in northing, in the right quadrant.

What is the reverse bearing?

The bearing of the line the other way, which is 180 degrees different.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any surveying text (bearings and joins).

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