Horizon Line Calculator

Measure horizon distance, dip angle, and hidden height. Add refraction, target height, and camera view. See your horizon line instantly with clean results today.

Advanced Horizon Line Calculator

Use eye height above water, ground, or surface.
Optional. Use mast, cliff, building, or object height.
Optional. Enter known range to test visibility.
Default is mean Earth radius.
Common value is 0.13 for standard air.
Used for horizon line pixel row.
Enter degrees for camera or scene view.
Use positive values when the camera tilts downward.
Reset

Example Data Table

These examples use Earth radius 6,371 km and no target height.

Case Eye Height Refraction Factor Approx Horizon Distance Use Case
Beach viewer 1.7 m 0.13 5.0 km Walking and shore view
Small boat deck 3 m 0.13 6.6 km Marine observation
Cliff view 50 m 0.13 27.1 km Photography planning
High tower 150 m 0.13 46.9 km Lookout estimation

Formula Used

Effective radius with refraction: R_eff = R / (1 - k)

Straight horizon distance: d = sqrt(2 × R_eff × h + h²)

Surface arc distance: s = R_eff × arccos(R_eff / (R_eff + h))

Dip angle: dip = arccos(R_eff / (R_eff + h))

Combined visibility range: s_total = s_observer + s_target

Image horizon row: row = imageHeight / 2 - ((pitchDown - dipDeg) / verticalFov) × imageHeight

Here, R is radius, h is eye height, and k is the refraction factor. A value of zero turns refraction into pure geometry.

How to Use This Calculator

  1. Enter observer eye height above the local surface.
  2. Select the matching unit for height.
  3. Add target height and distance when testing visibility.
  4. Keep the default radius for Earth, or enter another radius.
  5. Choose refraction settings for standard or clear geometry.
  6. Add camera values when you need a pixel row estimate.
  7. Press the calculate button to show results above the form.
  8. Download the result as CSV or PDF for records.

Horizon Line Planning Guide

Why the Horizon Changes

Horizon planning is useful for sailors, walkers, photographers, surveyors, and students. The visible horizon is not fixed. It changes when the eye height changes. A taller observer sees farther because the line of sight touches Earth at a later point.

How Refraction Affects Results

This calculator treats Earth as a sphere. It can also use an effective radius when refraction is included. Standard refraction bends light slightly toward Earth. That bend lets you see a little farther than pure geometry predicts. You can change the factor when local air layers are unusual.

Main Measurements

The main result is horizon distance. It is the ground distance from the observer to the tangent point. The tool also reports dip angle. Dip angle tells how far below true level the sea or land horizon appears. This helps with photography, mapping, and camera framing.

Target Visibility

Advanced fields add target height and target distance. A target has its own horizon distance. When both horizon distances overlap, the target should be visible in simple clear-air geometry. When the target is beyond that limit, the hidden height estimate shows how much may fall below the curve.

Image Placement

The image line option is for visual work. Enter image height, vertical field of view, and camera pitch. The calculator estimates the pixel row where the horizon line should appear. A level camera places the horizon slightly below center because of dip. A downward tilted camera moves it upward.

Practical Limits

Results are estimates, not legal survey data. Real visibility depends on haze, waves, terrain, temperature gradients, lens distortion, and exact elevation. Use verified geodetic tools for navigation or engineering. Use this page for fast planning, learning, and layout checks.

Best Input Tips

For best results, measure observer height carefully. Use eye height, not total body height. Choose a realistic Earth radius. Keep units consistent by using the unit selectors. Compare several refraction values when conditions are changing.

Exporting Results

You can use the example table to understand common cases. A person near the beach sees only a short range. A cliff, tower, drone, or ship bridge extends the view greatly. Export the result after each calculation. The files are useful for notes, lesson pages, and repeated field checks. They also support simple client reports.

Frequently Asked Questions

1. What does a horizon line calculator measure?

It measures how far the visible horizon is from your eye height. This version also estimates dip angle, target visibility, hidden height, and image line position for a camera frame.

2. Should I enter body height or eye height?

Enter eye height above the local surface. For a standing person on a beach, eye height is usually lower than total body height. For a boat or tower, add deck or platform height.

3. What is the standard refraction factor?

A common simple value is 0.13. It increases the effective radius and usually gives a longer visible range. Real air conditions can be different, so compare values when accuracy matters.

4. Why are straight and surface distances different?

Straight distance is the direct line from your eye to the tangent point. Surface distance follows the curved ground or sea arc. For normal eye heights, the two values are very close.

5. How does target height change visibility?

A tall target has its own horizon distance. Add the observer horizon and target horizon together. If the target is within that combined range, it may be visible in clear conditions.

6. What does hidden height mean?

Hidden height is the estimated part of a distant object that falls below curvature from your viewpoint. It is a geometric estimate and may differ when refraction or terrain changes.

7. How is the image horizon row useful?

It helps place the horizon line in a photo, render, sketch, or planning frame. Enter image height, vertical field of view, and camera pitch to estimate the row location.

8. Can I use this for navigation?

Use it for learning and planning only. Navigation, surveying, aviation, and marine safety need verified instruments, charts, local conditions, and professional geodetic methods.

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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.