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Calculating reach for wildlife photography

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Bird and wildlife photographers are concerned with the reach of a camera and lens setup.

Let’s define reach as the number of pixels per degree. If you’re a bird photographer, more is generally better. Here’s how to calculate reach given the focal length of the lens and the pixel pitch of the sensor.

Let’s define reach as the number of pixels per degree of horizontal field of view. To derive this, we start with basic geometry.

Imagine a right triangle formed by:

  • The focal length f of the lens (in mm),

  • Half the width on the sensor that corresponds to 1 degree of field of view,

  • And the angle of 0.5 degrees (half of 1° field of view).

half_field_mm = f × tan(0.5°)

Double that to get the full extent of a 1-degree field on the sensor:

field_width_mm = 2 × f × tan(0.5°)

Convert Field Width to Pixels

Let p be the pixel pitch in millimeters per pixel. Then:

pixels_per_degree = field_width_mm / p
= (2 × f × tan(0.5°)) / p

Since:

tan(0.5°) ≈ 0.00872687

The expression becomes:

pixels_per_degree ≈ (2 × f × 0.00872687) / p
≈ (0.0174533 × f) / p
pixels_per_degree ≈ (f / p) × (π / 180)
This equation reflects two intuitive properties:
  • Increasing the focal length increases reach (you’re zooming in).

  • Decreasing the pixel pitch increases reach (you’re sampling more finely).

For a 500 mm lens and a sensor with 4.6 µm pixels:

p = 0.0046 mm

f = 500 mm

Reach ≈ (500 / 0.0046) × 0.01745 ≈ 1,896 pixels per degree

Here are the approximate reach values (pixels per degree of field of view) for various camera formats using a 500 mm lens with typical pixel pitches for each class:

Camera Format Pixel Pitch Reach (pixels/degree)
Micro Four Thirds (20 MP) 3.3 µm 2,644
APS-C (24 MP) 3.9 µm 2,238
Full Frame (45 MP) 4.4 µm 1,983
GFX 100 (102 MP, 33×44 mm) 3.76 µm 2,321

Interpretation

  • The smaller formats (like MFT) offer greater reach due to finer angular resolution per pixel.

  • Despite the GFX 100’s massive pixel count, its larger sensor means each pixel covers a wider angle than smaller formats — but it still outperforms full-frame due to smaller pitch.

  • Of course, the Sony a7RIV and the GFX 100x have the same reach, since they have the same pixel pitch.

Comments

  1. Hi Jim,
    Thanks for all your tests and posting here, very interesting to read sound engineering material, at least on the usage and characterization side of this field
    That said, are you sure about this formula ? Either I misunderstood what you mean by pixels per degree or there must be something wrong, as increasing focal length should increase Reach as you defined, not reduce it.

    Reply

      • Thanks for the reworked article with detailed reasoning leading to the corrected formula and interpretation ! Mistakes happen, especially when you actually do stuff and go off the well beaten path…

        If I understand this correctly, this assumes a subject at infinity (or “far enough”), and small angles linear approximation. Which is perfectly suitable in the context of distant wildlife shot at long focal lengths, but would that mean that one should not generalize to short focal lengths and subjects far from optical center ?

        Reply

        • If I understand this correctly, this assumes a subject at infinity (or “far enough”), and small angles linear approximation. Which is perfectly suitable in the context of distant wildlife shot at long focal lengths, but would that mean that one should not generalize to short focal lengths and subjects far from optical center ?

          Yes. You understand the limitations perfectly.

          Reply

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Unless otherwise noted, all images copyright Jim Kasson.