Compute distance modulus, telescope magnification and exit pupil, Dawes and Rayleigh diffraction limits, spherical angular separation, equatorial coordinate conversions, and extended-object surface brightness contrast directly in your browser.
Interactive astronomy calculator for apparent magnitude (m), absolute magnitude (M), distance modulus (m - M), extinction (Av), and distance in pc and ly.
Governing Relation: μ = m − M − A_V = 5 log₁₀(d_pc) − 5 ⇔ d_pc = 10^((m − M − A_V + 5) / 5) ; d_ly = 3.2615638 × d_pc
Calculate telescope magnification, focal ratio, exit pupil diameter, true field of view (TFOV), and Dawes/Rayleigh resolution limits for any eyepiece.
Governing Relation: M = F_scope / F_ep ; f/# = F_scope / D ; Exit Pupil = D / M ; TFOV = AFOV / M ; Dawes = 116″ / D_mm
Estimate naked-eye and telescopic stellar limiting magnitude from aperture diameter, sky brightness (Bortle class / SQM), magnification, and observer pupil.
Governing Relation: NELM ≈ 7.93 − 5 log₁₀(10^(4.316 − S_sky/5) + 1) ; m_limit ≈ NELM + 5 log₁₀(D_scope / d_pupil) + 2.5 log₁₀(M / M_min) × k
Compute exact spherical angular separation between two RA/Dec coordinates and convert apparent angular size and distance into physical diameter in pc and ly.
Governing Relation: cos(θ) = sin δ₁ sin δ₂ + cos δ₁ cos δ₂ cos(α₁ − α₂) ; Physical Diameter D = 2 d tan(θ / 2) ≈ d × (θ_arcsec / 206,265)
Convert J2000 equatorial coordinates between sexagesimal (HH:MM:SS / DD:MM:SS) and decimal degrees, and compute meridian transit altitude for any latitude.
Governing Relation: α_deg = 15 × (H + M/60 + S/3600) ; δ_deg = sgn × (|D| + M′/60 + S″/3600) ; h_max = 90° − |φ_obs − δ| ; Airmass X ≈ sec(z)
Calculate extended object surface brightness (mag/arcsec²) from integrated magnitude and ellipse axes, and evaluate visual contrast against sky brightness.
Governing Relation: Area (arcsec²) = (π / 4) × a′ × b′ × 3600 ; S_obj = m_total + 2.5 log₁₀(Area) ; Contrast Ratio = 10^(−0.4 × (S_obj − S_sky))
