Earth Curvature Calculator

Calculate curve drop, bulge, horizon, and hidden object height. Adjust units, radius model, and refraction. Export clean field results for careful planning and review.

Advanced Calculator

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Example Data Table

Distance Observer Height Target Height Refraction Typical Use
10 km 2 m 20 m 0.13 Lake view or shoreline check
20 mi 6 ft 100 ft 0.13 Distant building visibility
5 nmi 10 m 30 m 0 Pure geometric navigation estimate

Formula Used

Effective radius: Re = R / (1 - k)

Arc angle: theta = d / Re

Exact tangent drop: drop = Re × (1 - cos(theta))

Approximate tangent drop: drop ≈ d² / (2 × Re)

Chord length: chord = 2 × Re × sin(theta / 2)

Midpoint bulge: bulge = Re - sqrt(Re² - (chord / 2)²)

Horizon distance: horizon = Re × arccos(Re / (Re + h))

Hidden height: hidden = Re × (sec(beta) - 1), after the observer horizon.

How to Use This Calculator

Enter the surface distance between the observer and target. Choose the matching distance unit.

Add observer height above the local surface. Add target height if visibility matters.

Select a radius model. Use custom radius for special planetary or geodetic checks.

Enter a refraction coefficient. Use 0 for pure geometry. Use 0.13 for common standard refraction estimates.

Press Calculate. Review drop, bulge, horizon distance, hidden height, and visibility status.

Use CSV or PDF export to save results for reports, notes, or comparison tables.

Earth Curve Planning Guide

Earth curvature matters whenever distance is large. A road, lake, sea view, antenna path, or survey line may look flat nearby. Over many kilometers, the surface falls away from a straight tangent line. This calculator turns that curve into useful numbers. It helps compare drop, midspan bulge, horizon range, and hidden height.

What Curvature Means

Curvature is the amount a spherical surface bends. Earth is not a perfect sphere. It is slightly wider at the equator. Still, a spherical model works well for many field estimates. The calculator includes mean, equatorial, polar, and custom radius choices. That makes it useful for simple checks and technical comparisons.

Distance And Drop

The main input is surface distance. The calculator converts miles, kilometers, nautical miles, meters, or feet into one working unit. Exact drop uses the cosine relation for an arc on a circle. The common eight inches per mile squared rule is only an approximation. It is convenient for short distances, but it grows less accurate across long spans.

Observer Height And Horizon

Height changes what can be seen. A taller observer sees farther because the line of sight touches the curved surface later. The same idea applies to a tower, ship, mountain, or building. The calculator combines observer and target horizon distances. It then estimates how much of the target may be hidden beyond the geometric horizon.

Refraction And Practical Use

Air bends light slightly downward in many normal conditions. This makes the visible horizon appear farther than pure geometry predicts. Surveyors often model this with an effective Earth radius. A common coefficient is 0.13. Conditions can change quickly near hot ground, cold water, or layered air. Treat refraction as an estimate, not a fixed truth.

Good Data Habits

Use consistent measurements. Check whether distance is along the surface, not a map scale error. Enter realistic heights above the local surface. Compare exact and approximate drop. Save the CSV or PDF when documenting results. For engineering, navigation, or legal survey work, verify values with professional instruments and local geodetic data.

Small changes can matter. One extra meter of eye height may reveal distant features. A changed radius setting can also shift long range estimates slightly today.

FAQs

What does Earth curvature drop mean?

It is the vertical fall of Earth’s surface below a straight tangent line over a given surface distance.

Is the result exact?

The exact result is based on a spherical Earth model. Real terrain, geoid variation, and atmosphere can change field observations.

What refraction value should I use?

Use 0 for pure geometry. Use 0.13 for a common standard atmosphere estimate. Local conditions may differ.

Why is observer height important?

Higher eyes see farther over the curve. Even small height changes can increase horizon distance noticeably.

What is hidden height?

Hidden height estimates how much of a distant object is blocked below the observer’s geometric horizon.

Can this calculator be used for oceans?

Yes. It is useful for sea horizons, ships, islands, and lighthouses when distance and heights are known.

Does terrain affect the answer?

Yes. Hills, waves, buildings, and elevation changes can dominate the geometric curvature result.

Why export CSV or PDF?

CSV helps spreadsheet analysis. PDF gives a simple record for reports, field notes, or client summaries.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.