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Fisheye to Rectilinear Angle Calculator

Enter your fisheye lens angle of view and focal length to calculate the rectilinear equivalent angle, compression ratio, barrel distortion, and projected sensor coverage.
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Luis GonzalezCreated by Luis GonzalezLast updated:

How to Use This Calculator

  1. 1

    Enter Fisheye Angle of View (°)

    Input the total diagonal angle of view captured by your fisheye lens, typically 100° to 180°.

  2. 2

    Specify Focal Length (mm)

    Provide the focal length of your fisheye lens in millimeters, usually between 4 mm and 16 mm.

  3. 3

    Review Rectilinear Equivalence

    Examine the calculated rectilinear equivalent angle, compression ratio, and barrel distortion to understand how your fisheye image translates to a conventional perspective.

Example Calculation

A photographer wants to understand how a 120° fisheye lens with an 8mm focal length compares to a standard rectilinear lens.

Fisheye Angle of View (°)

120

Focal Length (mm)

8

Results

92.4°

Tips

Understand Projection Types

Fisheye lenses use various projection types (stereographic, equisolid, equidistant, orthographic) which subtly affect distortion. This calculator assumes an equidistant projection, a common type. For critical applications, verify your lens's specific projection.

Use for Panorama Stitching

Fisheye lenses are excellent for capturing ultra-wide panoramas with fewer shots. Use the rectilinear equivalent angle to plan overlaps and stitch points more effectively in post-processing software.

Consider Sensor Size Impact

The effective angle of view of any lens, including fisheye, changes with sensor size. A fisheye on an APS-C sensor will have a narrower effective field of view than on a full-frame sensor, impacting the perceived distortion and coverage.

Bridging Perspectives: Fisheye to Rectilinear Angle Conversion

The Fisheye to Rectilinear Angle Calculator is an indispensable tool for photographers, cinematographers, and virtual reality developers working with ultra-wide-angle optics. This calculator translates the extreme perspective of a fisheye lens into its rectilinear equivalent, quantifies barrel distortion, and estimates the image circle radius for any given focal length. Understanding this conversion is critical for planning shots, correcting images in post-production, or comparing the coverage of diverse lens types, especially as fisheye lenses often capture angles between 100° and 180° in 2025.

The Geometry of Wide-Angle Lenses

The fundamental difference between fisheye and rectilinear lenses lies in their optical projection. A rectilinear lens is designed to maintain straight lines straight, mimicking human perception, but achieves this by sacrificing some field of view at wider angles. A fisheye lens, conversely, prioritizes capturing an extremely wide field of view, often exceeding 180 degrees, by allowing significant barrel distortion. This geometric trade-off means that understanding the mathematical relationship between the two is key to effectively utilizing each lens type for its intended purpose, from architectural photography to immersive virtual tours.

The Mathematical Transformation of Fisheye Perspective

The Fisheye to Rectilinear Angle Calculator employs trigonometric functions to accurately convert the curved projection of a fisheye lens into an equivalent rectilinear angle and quantify the associated distortion. The calculation typically assumes an equidistant fisheye projection model.

Key formulas used are:

  1. Half-Angle in Radians: Half Angle (rad) = (Fisheye Angle of View / 2) × (π / 180)
  2. Image Circle Radius (Fisheye Projection): Fisheye Radius (R) = Focal Length (mm) × Half Angle (rad)
  3. Rectilinear Equivalent Angle: Rectilinear Angle (deg) = 2 × arctan(R / Focal Length (mm)) × (180 / π)
  4. Barrel Distortion (%): Barrel Distortion = ((Fisheye Angle - Rectilinear Angle) / Fisheye Angle) × 100

These equations allow for a precise comparison of how much visual information is "compressed" or distorted by the fisheye effect.

💡 To understand how sensor size and focal length affect depth of field, our Circle of Confusion Calculator is an invaluable resource.

Converting a Fisheye's View to Rectilinear

Let's consider a photographer using an 8mm fisheye lens with a 120° angle of view. They want to know its rectilinear equivalent and distortion.

  1. Half-Angle in Radians: (120° / 2) × (π / 180) = 60° × (π / 180) = π/3 radians ≈ 1.047 radians
  2. Fisheye Radius (R): 8 mm × (π/3) = 8.378 mm
  3. Rectilinear Equivalent Angle: 2 × arctan(8.378 mm / 8 mm) × (180 / π) = 2 × arctan(1.047) × (180 / π) ≈ 2 × 0.8067 rad × 57.2958 ≈ 92.4°
  4. Barrel Distortion: ((120° - 92.4°) / 120°) × 100 = (27.6 / 120) × 100 = 23.0%

The 120° fisheye lens with an 8mm focal length has a rectilinear equivalent angle of approximately 92.4° and exhibits about 23.0% barrel distortion. This means the fisheye captures a significantly wider field of view than a rectilinear lens of the same focal length, but with considerable curvature.

💡 For analyzing musical intervals and harmonies, our Chord Frequency Ratio Calculator applies mathematical principles to audio.

Formula Variants in Lens Projection

While the equidistant projection model is commonly assumed for fisheye lenses in many calculations, it's not the only type. Other common fisheye projection models include stereographic, equisolid angle, and orthographic, each producing slightly different levels of distortion and field of view for a given focal length. For instance, a stereographic projection (often considered the most "natural" looking fisheye) maps angles such that areas near the edge are less stretched than in an equidistant projection, resulting in a different rectilinear equivalent and distortion percentage. The formula for the image radius (R) in a stereographic fisheye is R = 2f * tan(θ/2), where f is focal length and θ is the half-angle of view. An equisolid angle projection (common in scientific applications) preserves the relative areas of objects within the scene, with R = 2f * sin(θ/2). These variations mean that while the core concept of converting fisheye to rectilinear remains, the specific mathematical coefficients and functions will differ depending on the lens's optical design, which can be crucial for precise photogrammetry or scientific imaging.

Frequently Asked Questions

What is the difference between a fisheye and a rectilinear lens?

A fisheye lens produces a highly distorted, ultra-wide-angle image, often exceeding 180 degrees, with curved lines and a bulging effect, designed to capture as much of the scene as possible. A rectilinear lens, in contrast, corrects for distortion, rendering straight lines as straight and preserving a more natural, human-eye perspective, though with a narrower field of view for the same focal length.

How does the Fisheye to Rectilinear Angle Calculator help photographers?

The Fisheye to Rectilinear Angle Calculator helps photographers understand the effective field of view and the degree of distortion when using a fisheye lens. It converts the fisheye's extreme angle into a comparable rectilinear angle, quantifies barrel distortion, and estimates the image circle. This allows for better planning of shots, understanding post-processing needs, and comparing fisheye coverage to conventional wide-angle lenses.

What is 'barrel distortion' and why is it prominent in fisheye lenses?

Barrel distortion is a type of optical aberration where straight lines appear to bulge outwards, especially at the edges of the image. It is prominent in fisheye lenses because they are designed to compress a very wide field of view into a flat image sensor, achieving angles up to 180 degrees or more. This compression inherently causes objects away from the image center to appear increasingly curved and expanded, creating the characteristic 'fisheye' effect.