Right Ascension and Declination Converter
Convert Right Ascension (RA) and Declination (Dec) between Hours-Minutes-Seconds / Degrees-Minutes-Seconds, decimal degrees, and radians.
Right Ascension (RA)
Declination (Dec)
Formulas
Right Ascension — HMS ↔ Decimal Degrees:
RA (°) = (H + M/60 + S/3600) × 15
where 1 hour of RA = 15° (since 360° / 24 h = 15°/h)
Inverse: H = floor(RA° / 15), M = floor(frac × 60), S = frac₂ × 60
Declination — DMS ↔ Decimal Degrees:
Dec (°) = sign × (|D| + M/60 + S/3600)
where sign is determined by the sign of the degrees field
Degrees ↔ Radians:
rad = deg × π / 180 | deg = rad × 180 / π
Valid Ranges:
RA: 0h 0m 0s – 23h 59m 59.999s | 0° – 359.9999° | 0 – 2π rad
Dec: −90° 0' 0" – +90° 0' 0" | −90° – +90° | −π/2 – +π/2 rad
Assumptions & References
- Right Ascension is measured eastward along the celestial equator from the vernal equinox (First Point of Aries), ranging 0–24 hours (0°–360°).
- Declination is measured north (+) or south (−) of the celestial equator, ranging −90° to +90°.
- The conversion factor 15°/hour arises because Earth rotates 360° in 24 hours: 360 / 24 = 15.
- When entering DMS for Declination, the sign (±) is applied only to the degrees field; minutes and seconds are always non-negative.
- Coordinates are assumed to be in the same equatorial reference frame (e.g., J2000.0); no epoch precession is applied.
- Reference: IAU SOFA Library; Astronomical Almanac; Green, R.M. — Spherical Astronomy (Cambridge University Press, 1985).