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Curvature And Refraction Correction Calculator

Work out curvature and refraction correction instantly with clear inputs, formula shown and shareable results.

About Curvature And Refraction Correction Calculator

Over long sights the earth curves away from the level line, making staff readings too large by 0.0785 d² metres with distance in kilometres. Atmospheric refraction bends the line of sight downward and partly offsets it, conventionally by one seventh, so the combined correction is about 0.0673 d² and is subtracted from the observed reading.

Formulas

Curvature

c = 0.0785 d² metres, d in kilometres

Combined

Combined = curvature x (1 - refraction coefficient), about 0.0673 d²

Worked example

With the default values below, Curvature And Refraction Correction Calculator returns Combined curvature and refraction correction of 0.15190. Change any input above and every figure here is recalculated in your browser.

Inputs used

Sight distanceminimum 0.001 km
1.5 km
Refraction coefficientaccepts 0.01–0.5
0.14

Results

Combined curvature and refraction correction
0.15190 m
Curvature correction
0.17662 m
Refraction correction
0.02473 m
Combined correction in millimetres
151.90 mm

Step by step

  1. 1Values used
  2. 2Curvature
  3. 3Combined
  4. 4Combined curvature and refraction correction= 0.15190 m
  5. 5Curvature correction= 0.17662 m
  6. 6Refraction correction= 0.02473 m
  7. 7Combined correction in millimetres= 151.90 mm

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is the Curvature And Refraction Correction figure worked out?

c = 0.0785 d² metres, d in kilometres. Over long sights the earth curves away from the level line, making staff readings too large by 0.0785 d² metres with distance in kilometres.

When can the correction be ignored?

When backsight and foresight distances are equal, because the error cancels. That is why balancing sight distances is standard levelling practice and why the correction matters mainly for trigonometric heighting.

What values do I need to enter?

This calculator takes 2 inputs: Sight distance, Refraction coefficient. The pre-filled defaults are a realistic worked example — replace them with your own site or project figures.

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