Prayer Times Calculations

Calculation Parameters

Date

Calculation Method

Latitude

Longitude

Elevation (m)

Timezone (UTC offset)

DST Active

📍 Calculation Inputs

1Julian Date Calculation

The Julian Date is a continuous count of days since January 1, 4713 BC (proleptic Julian calendar). It's used for astronomical calculations.

Formula:

JD = JD(date) - longitude / (15 × 24)

The longitude adjustment converts the Julian date to the local meridian

2Solar Position

Calculate the sun's position using USNO low-precision formulas (accurate to within 1 arcminute for 1950-2050).

2.1 Days since J2000.0

Formula:

D = JD - 2,451,545.0

2.2 Mean Anomaly

Formula:

g = 357.529° + 0.98560028° × D (mod 360°)

2.3 Mean Longitude

Formula:

q = 280.459° + 0.98564736° × D (mod 360°)

2.4 Ecliptic Longitude

Formula:

L = q + 1.915° × sin(g) + 0.020° × sin(2g) (mod 360°)

2.5 Solar Declination

Formula:

δ = arcsin(sin(ε) × sin(L))

where ε = 23.439° - 0.00000036° × D (obliquity of ecliptic)

2.6 Equation of Time

Formula:

EqT = q/15 - fixhour(RA)

where RA = arctan2(cos(ε) × sin(L), cos(L)) / 15

3Prayer Times Calculation

Note: Prayer times are calculated based on the sun's position relative to the horizon. Different calculation methods use different sun angles for Fajr and Isha.

Calculation Parameters

📍 Calculation Inputs

1Julian Date Calculation

2Solar Position

2.1 Days since J2000.0

2.2 Mean Anomaly

2.3 Mean Longitude

2.4 Ecliptic Longitude

2.5 Solar Declination

2.6 Equation of Time

3Prayer Times Calculation

4Final Prayer Times