AstroCalc

Astronomy & cosmology, at your fingertips.

LOCAL CALCULATIONS · NO DATA SENT
Research toolkit / 01

Measure the Universe.

Quick, transparent calculators for common astronomical conversions. Cosmological quantities share one parameter set; results are estimates under the model shown.

Flat ΛCDM · numerical integration

Cosmology & distances

Cosmology engine

Set the background cosmology used by all redshift-based distance and time tools.

Shared parameters

Assumes spatially flat ΛCDM: ΩΛ = 1 − Ωm − Ωr. Radiation defaults to zero for low-redshift work. A negative ΩΛ is permitted mathematically, but may not describe the cosmology you intend.

Current model: H₀ = 70, Ωm = 0.30, Ωr = 0.00, ΩΛ = 0.70

Redshift → distances & time

Comoving, angular-diameter and luminosity distances, plus lookback time and cosmic age.

ΛCDM

Angular size ↔ physical size

Convert an angular diameter to a transverse physical size using Dₐ(z).

Small-angle

Flux ↔ luminosity

Bolometric or band-integrated flux and luminosity, without a K-correction.

Inverse-square law

Distance modulus

Apparent ↔ absolute magnitude from luminosity distance.

No extinction / K-correction

Redshift ↔ spectral wavelength

Observed/rest wavelength conversion for spectral features.

Spectroscopy

Redshift ↔ recession velocity

Special-relativistic Doppler conversion for a radial velocity interpretation.

Not Hubble flow at high z

This is a Doppler-equivalent velocity, not a general cosmological recession velocity. For nearby objects, peculiar velocity corrections and the adopted frame (heliocentric, barycentric, CMB) matter.

Photometry & spectra

AB magnitude ↔ flux density

Convert AB magnitude and fν in Jy, mJy or μJy.

AB system

Galactic foreground extinction

Estimate Aᵦ = Rᵦ × E(B−V) using a selectable coefficient.

Foreground only

Coefficients are approximate and depend on the adopted extinction law, bandpass and source SED. Apply to Galactic foreground only; internal attenuation is a separate correction.

Coordinates & time

RA / Dec ↔ decimal degrees

Parse sexagesimal coordinates with sign and range checks.

ICRS-style input

Angular separation

Great-circle separation between two sky positions.

Spherical geometry

Julian Date / Modified Julian Date

Calendar date and time in UTC → JD and MJD.

UTC input

This uses the browser's date input fields as UTC calendar components; leap-second representation is not supported.

Galactic ↔ equatorial coordinates

Transform ICRS/J2000 equatorial coordinates to Galactic longitude and latitude.

Fixed rotation

Observing conditions

Airmass

Kasten–Young approximation from target altitude.

Atmosphere

The approximation is not intended for targets at or below the horizon; near-horizon atmospheric conditions are especially uncertain.

Quick unit conversions

Useful constants and common distance conversions.

Exact factors