Interactive Observational Astronomy Calculator

Camera Pixel Scale & Sensor FOV Calculator

Compute angular pixel scale (″/px), sensor field of view, and seeing sampling regime (undersampled, well-sampled, oversampled) from telescope focal length and sensor geometry.

Governing Formula: Pixel Scale s = 206.265 × p_μm / F_mm (″/px) ; FOV_width = (N_x × s) / 3600° ; Sampling Ratio = FWHM_seeing / s

Interactive Calculation Workbench

Computed Output: Pixel Scale s = 0.97″/px · FOV Width = 48.5′ (0.81°) · Sampling = 2.58 px/FWHM (Well-Sampled)

Derivation & Physical Background

Matching a CMOS or CCD detector to a telescope focal length governs both the angular field of view on the sky and whether fine stellar and planetary detail is properly sampled according to the Shannon-Nyquist theorem. A pixel scale s = 206.265 × p_μm / F_mm converts physical pixel pitch (in micrometers) and focal length (in millimeters) into arcseconds per pixel.

Under typical nighttime seeing (FWHM ≈ 2.0″–3.0″), optimal deep-sky sampling occurs when the stellar FWHM spans 2.0 to 3.5 pixels. Coarse pixel scales (< 1.2 px per FWHM) produce boxy, undersampled stars, whereas ultra-fine scales (> 4.5 px per FWHM) spread photon flux across many pixels without adding spatial resolution.

Worked Benchmark Example: A 3.76 μm pixel CMOS sensor (3000 × 3000 pixels) on an F = 800 mm refractor yields a pixel scale of s = 206.265 × 3.76 / 800 = 0.97″/px, a 48.5′ × 48.5′ field of view, and 2.58 pixels per FWHM under 2.5″ seeing (ideal Nyquist sampling).

Assumptions, Approximations & Validity Limits

  • Uses the paraxial small-angle plate scale formula; wide-field camera lenses with rectilinear or fisheye projection deviate by several percent near the frame corners.
  • Assumes unbinned 1×1 readout; 2×2 hardware or software binning doubles the effective pixel pitch p_μm.
Reference Guide

Angular Size, Separation & Field of View

How angular diameter (degrees, arcminutes, arcseconds), spherical angular separation, and small-angle physical diameter relate to telescope field of view.

Barred spiral galaxy (Local Group largest spiral)

Andromeda Galaxy (Messier 31 / NGC 224)

Coordinates, Cepheid/TRGB distance (765 kpc / 2.50 Mly), magnitude 3.44, blueshift (−300 km/s), and observing guide for Andromeda (M31).

Diffuse H II emission and reflection nebula

Orion Nebula (Messier 42 / NGC 1976)

Coordinates, VLBI/Gaia distance (412 pc), Trapezium ionizing cluster, and visual observing guide for the Orion Nebula (M42) in Orion.

Interacting grand-design spiral galaxy pair

Whirlpool Galaxy (Messier 51 / NGC 5194)

Coordinates, SN II-P / TRGB distance (8.58 Mpc / 28.0 Mly), grand-design spiral arms, NGC 5195 tidal companion, and observing guide for M51.

Planetary nebula (bipolar barrel viewed nearly pole-on)

Ring Nebula (Messier 57 in Lyra)

Coordinates, Gaia DR3 central star distance (787 pc), magnitude 8.8, and telescope observing guide for the Ring Nebula (M57) in Lyra.

Scientific Standards & References

  • Revised New General Catalogue and Index Catalogue (RNGC/IC) (2024/2026 edition): Steinicke, W. 2010, Observing and Cataloguing Nebulae and Star Clusters (Cambridge Univ. Press); Verga, M. OpenNGC (CC-BY-SA 4.0 / data tables) — Wolfgang Steinicke / OpenNGC
  • SIMBAD Astronomical Database (CDS) (2026-10 release): Wenger, M., et al. 2000, A&AS, 143, 9 (The SIMBAD astronomical database) — Centre de Données astronomiques de Strasbourg