What Is a Fisheye Lens? Types, Projections, Field of View

A fisheye lens is an ultra-wide lens that records about 180° or more by letting straight lines curve instead of correcting them. A circular fisheye draws a round image with black corners, while a diagonal (full-frame) fisheye fills the whole frame and reaches 180° only from corner to corner. Which of the two you get depends on the focal length, the sensor size and the lens projection.

How a fisheye lens works

A normal wide-angle lens uses a rectilinear projection: the distance of an image point from the center is r = f × tan θ, where θ is the angle from the optical axis. That keeps straight lines straight, but r grows without limit as θ approaches 90°, so a rectilinear lens cannot cover a full hemisphere^[1]. Canon describes the design goal accordingly: wide-angle lenses suppress edge distortion with special elements such as aspherical ones, while fisheye lenses do not suppress it^[2].

A fisheye uses a different mapping that squeezes the outer parts of the view so that 180° fits on a flat sensor. The idea goes back to R. Hill's 1924 lens for whole-sky photographs, whose negative front element and reverse-telephoto layout are still used in every fisheye design^[1]. Three things follow from the construction:

• Lines that pass through the image center stay straight. All others bend, more strongly toward the edge.
• Focal lengths are very short, so depth of field is large and refocusing is rarely needed^[1].
• The front element bulges strongly, so screw-in front filters usually do not fit (see below).

Fisheye projections: equidistant, equisolid, stereographic, orthographic

"Fisheye" is not one fixed distortion. The standard mapping functions below relate the image distance r to the angle θ and the focal length f^[1]:

Projection	Formula	Character	r at 90° off axis (in units of f)
Rectilinear (normal lenses)	r = f × tan θ	Straight lines stay straight	not reachable
Equidistant	r = f × θ	Image distance proportional to the angle	1.57
Equisolid (equal area)	r = 2f × sin(θ/2)	Equal solid angles take equal image area	1.41
Stereographic	r = 2f × tan(θ/2)	Least barrel distortion of the four	2.00
Orthographic	r = f × sin θ	Strongest edge compression, 180° maximum	1.00

The last column is calculated from the formulas (θ in radians for the equidistant case). The higher the value, the less the edge is squeezed. The University of Arizona thesis rates stereographic as the projection with the least barrel distortion and orthographic with the most, with equidistant and equisolid in between^[1].

Most photographic fisheye lenses are designed around the equisolid projection, a few use the others, and manufacturers often modify the standard curves slightly. The thesis shows this for the Nikkor 16 mm f/2.8 fisheye, whose measured mapping deviates from pure equisolid^[1]. Canon, on the other hand, states that its RF 7-14mm F2.8-3.5L Fisheye STM uses equidistant projection, which enables its 180° VR video conversion^[3].

For you this means two things. Judge a fisheye by its stated angle of view, not by its focal length alone, because the same focal length gives different angles under different projections. And if you stitch panoramas or process VR footage, the projection is the setting your software asks for.

Circular vs. diagonal fisheye

A circular fisheye projects an image circle smaller than the sensor. Canon describes it as 180° across the whole periphery, horizontally, vertically and diagonally, with corner vignetting that creates a tunnel-vision effect^[2]. A diagonal fisheye, also called full-frame fisheye, enlarges the image so it covers the entire frame and reaches roughly 180° along the diagonal only^[2]. "Full-frame" here means the picture fills the frame. It does not mean the lens is made for a full-frame sensor.

Some lenses go past 180°. The Canon RF 5.2mm F2.8L Dual Fisheye offers a 190° field of view^[4], the Canon RF 7-14mm gives 190° at 7 mm^[3], and the Laowa 4mm f/2.8 is listed with 210° for Micro Four Thirds and APS-C cameras^[5].

Focal lengths by sensor size

The type you get depends on the sensor behind the lens. Canon puts it at around 8 mm for a circular image on full frame and around 15 mm (full frame) or 10 mm (APS-C) for a diagonal image^[2]. The table gives the focal lengths that an ideal equisolid lens needs for exactly 180°, calculated from the sensor dimensions:

Sensor	Circular, 180° circle fits the frame height	Diagonal, 180° corner to corner
Full frame (36 × 24 mm)	up to about 8.5 mm	about 15.3 mm
APS-C, 1.5x (Sony, Nikon, Fujifilm)	up to about 5.5 mm	about 10 mm
APS-C, 1.6x (Canon)	up to about 5.2 mm	about 9.5 mm
Micro Four Thirds (2x)	up to about 4.6 mm	about 7.7 mm

Real lenses deviate from this by a few millimeters or degrees. The Panasonic Lumix G Fisheye 8mm F3.5 is specified with a 180° diagonal angle of view on Micro Four Thirds^[6], while a pure equisolid mapping would give about 170° at 8 mm, so its projection differs a little from the ideal.

Fisheye zooms cover both looks on one full-frame lens. The Sony FE 8-14mm F3.5 Fisheye G goes from circular fisheye at 8 mm to diagonal fisheye at 14 mm^[7], the Canon RF 7-14mm does the same between 7 and 14 mm^[3], and the Nikon AF-S Fisheye NIKKOR 8-15mm f/3.5-4.5E ED is specified with a 180° circular image at 8 mm and a 180° diagonal image when zoomed in toward 15 mm. At exactly 15 mm the angle is slightly smaller, 175°^[8].

The same lens on a different sensor

A smaller sensor records only the center of the image circle. Canon points out that at 8 mm on an APS-C camera you will not get a distinct circular effect, because the field of view equals roughly 13 mm on full frame^[2]. Nikon specifies the same zoom with 180° to 110° on DX bodies, with 180° diagonal reached around the DX mark on the zoom ring^[8]. On full frame it is the other way round: an APS-C fisheye needs the camera's crop mode to avoid black edges, and you lose resolution (how crop mode works, APS-C vs. full frame).

Fisheye field of view: diagonal, horizontal and vertical

"180°" almost always refers to the diagonal, or to every direction in the case of a circular fisheye. The horizontal and vertical angles of a diagonal fisheye are smaller. Calculated for ideal equisolid lenses:

Lens and sensor	Diagonal	Horizontal	Vertical
Circular fisheye, 8 mm on full frame	180°	180°	180°
Diagonal fisheye, 15.3 mm on full frame	180°	144°	92°
Diagonal fisheye, 7.7 mm on Micro Four Thirds	180°	138°	101°
Full-frame 15 mm fisheye on APS-C (1.5x)	112°	92°	60°
For comparison: rectilinear 12 mm on full frame	122°	113°	90°
For comparison: rectilinear 20 mm on full frame	94°	84°	62°

On an APS-C body, a fisheye built for full frame therefore behaves like an ultra-wide with curved lines. The field of view simulator calculates rectilinear lenses only, so use it for the comparison rows, not for fisheyes.

Fisheye vs. ultra-wide lens

A rectilinear ultra-wide lens keeps lines straight and stretches the corners instead. A fisheye curves the lines and compresses the edges.

	Rectilinear ultra-wide	Fisheye
Straight lines	Stay straight	Curve, except those through the center
Typical full-frame focal length	12 to 20 mm	about 8 mm (circular), 12 to 16 mm (diagonal)
Diagonal angle on full frame	94° (20 mm) to 122° (12 mm)	180° or more
Filters	Often a front thread	Bulging front, usually no screw-in filters

On filters, Nikon states for the AF-S Fisheye NIKKOR 8-15mm that a filter cannot be attached^[8], while the Canon RF 7-14mm takes a rear drop-in filter^[3].

Can you remove the fisheye effect?

Partly. Photoshop's Adaptive Wide Angle filter has a Fisheye correction type for extreme curvature from fisheye lenses^[9]. A flat image cannot show 180° (tan θ is infinite at 90°), so the correction stretches the edges and crops the frame. If you want straight lines from the start, choose a rectilinear lens from the Sony E wide-angle page or the equivalent page of your mount.

When shooting, a level camera keeps the horizon through the image center straight. Tilting up or down bends it one way or the other.

What a fisheye is good for

• Interiors and tight spaces. One camera position can show a whole room, a staircase or a cathedral dome.
• Action and close-ups. With the subject near the center and the surroundings curving around it, sports and street scenes get a strong look.
• Sky and astro. A wide field captures large parts of the sky. The Hill lens of 1924 was designed for exactly that.
• 360° and VR. Circular and dual fisheyes feed panorama and VR workflows, for example the Canon RF 5.2mm F2.8L Dual Fisheye with its 190° view^[4].
• Landscape. With a level horizon and few straight lines, the curvature is less obvious.
• Creative portraits. Keep the person in the center and let the surroundings bend.

It is a poor choice when exact geometry matters, for example product shots, documentary architecture or close portraits of faces, where near parts of the face get enlarged.

What to look for when choosing a fisheye

1. Sensor coverage. A full-frame fisheye on APS-C is a narrower, curved ultra-wide, an APS-C fisheye on full frame needs crop mode. Use the tables above.
2. Circular or diagonal. Decide on the round image or the filled frame and check the stated angle of view.
3. Projection. Matters mainly for VR and stitching. Check whether the manufacturer states it.
4. Focus. Most fisheye lenses in our database are manual focus. Because of the large depth of field this is less of a limit than on other lenses: at 15 mm and f/8, focusing at about 0.95 m keeps everything from roughly 0.5 m to infinity acceptably sharp (calculated with a 0.03 mm circle of confusion on full frame).
5. Filters. Plan for rear drop-in or gelatin filters or none at all, see above.
6. Aperture and minimum focus distance. Both are listed for every lens on our data pages. Fast apertures matter for astro, short focus distances for the close-up look.

Browse the fisheye lenses by mount: Sony E, Canon RF, Canon EF, Nikon F and Micro Four Thirds. The overview of all lens types shows where fisheyes fit among the other categories.

Frequently asked questions

What is a fisheye lens used for?

For interiors, action shots, sky and astro photography, 360° and VR footage, and deliberately curved creative pictures. It is not meant for work that needs exact straight lines.

What is the difference between a circular and a diagonal fisheye?

A circular fisheye draws a round image with 180° in every direction and black corners. A diagonal fisheye fills the frame and reaches 180° only corner to corner. On full frame the circular type needs about 8 mm and the diagonal type about 15 mm.

What focal length is a fisheye lens?

It depends on the sensor and the projection. On full frame, around 8 mm for a circular image and around 15 mm for a diagonal one. On APS-C around 5.5 mm and 10 mm, on Micro Four Thirds about 4.6 mm and 7.7 mm.

What is the field of view of a fisheye lens?

Typically 180°, measured across the diagonal for a diagonal fisheye and in every direction for a circular one. Some lenses reach 190° or 210°. Horizontally, a diagonal fisheye on full frame covers about 144°.

Is a fisheye the same as a wide-angle lens?

No. Both are wide, but a wide-angle lens is built to keep straight lines straight, while a fisheye lets them curve to reach 180° and beyond. A rectilinear 12 mm lens covers about 122° diagonally on full frame.