HesapHanem

Setting Out Offset Calculator

Enter the centerline point, bearing and offset distance to set out the offset point.

How it is calculated

Enter the easting (cx) and northing (cy) of a point on the centreline, the centreline bearing in degrees, and the offset distance in metres. The bearing is an azimuth measured clockwise from grid north. A positive offset is to the right of the line when looking along the bearing; a negative offset is to the left. The tool turns the bearing 90° clockwise, b' = bearing + 90, and computes ΔE = offset × sin(b') and ΔN = offset × cos(b'). The new point is E = cx + ΔE and N = cy + ΔN. Results are in the unit you used for the offset and coordinates, shown to three decimals. The offset bearing shown is always bearing + 90, whatever the sign of the offset. It works on a flat grid and does not correct for scale factor or convergence.

Worked example

A centreline point at E 1000, N 2000 with a bearing of 30°, and a point 5 m to the right. The offset direction is 30 + 90 = 120°. ΔE = 5 × sin 120° = 4.330 and ΔN = 5 × cos 120° = −2.500. The new point is E = 1000 + 4.330 = 1,004.330 m and N = 2000 − 2.500 = 1,997.500 m. With an offset of −5 the point would be on the left, at E 995.670 and N 2,002.500.

Try this example →

Common mistakes

  • Entering the bearing as a mathematical angle measured anticlockwise from east. The bearing here is an azimuth clockwise from north, so a line running due east is 90, not 0.
  • Getting the side wrong. Positive is right when facing the direction of the bearing, and negative is left, not the other way round.
  • Swapping easting and northing in the centreline point. E (x) goes in cx and N (y) goes in cy, and a swap puts the point far away.
  • Entering the bearing in degrees-minutes-seconds format or gradians. The field takes decimal degrees, so 30°30′ is 30.5.
  • Reading the offset bearing as the direction of the left side. The tool always shows bearing + 90, the right-hand direction.

About this calculator

In surveying, setting out a point requires computing its coordinates from a known reference. Given a centerline point's coordinates and its bearing (direction), a point offset perpendicular to that line is found by adding an offset distance in the direction of the bearing rotated ±90°: E_offset = E + d·sin(bearing ± 90°) and N_offset = N + d·cos(bearing ± 90°), where d is the offset distance.

Land surveyors and construction engineers use this calculation constantly when marking out building corners, road edges, pipeline routes or fence lines relative to a surveyed centerline or baseline, since it lets a total station or GPS crew stake a precise point on the ground without needing to physically measure out from the centerline at every location.

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