DPC Angles by City & Month
All values on this page are computed from pray-calc v2.0.0 getAngles() using the 15th of each month in 2025. These are DPC model predictions — not empirically measured angles — except where noted.
How to read these tables
Fajr angle: the solar depression angle (degrees below the geometric horizon) at which the DPC model predicts true dawn (al-Fajr al-Sadiq) begins. The NREL SPA then computes the exact local time when the Sun reaches this altitude.
Isha angle: the depression angle at which the DPC model predicts night (disappearance of redness from the western sky) begins. A — indicates the Sun's minimum nocturnal altitude does not fall below the computed angle (summer perpetual twilight); Islamic authorities apply fallback rules in these cases.
Clipping: DPC outputs are clamped to [10°, 22°]. Values of 10.000 indicate the model computed a lower value that was clipped — this occurs at extreme latitudes in summer where the twilight physics produces angles below 10°. Real sky conditions at these times are ambiguous; the 10° floor represents the minimum physiologically meaningful "dark sky" threshold.
Fixed method reference:
- ISNA: 15°/15° (North America)
- MWL: 18°/17° (global default)
- Egypt: 19.5°/17.5°
- MUIS: 20°/18° (Malaysia/Singapore)
Northern Europe
Reykjavik, Iceland — 64.14°N, 21.90°W — elevation 18 m
At 64°N, summer sun barely grazes the horizon. Isha is unreachable for nearly the entire year. Fajr angles hit the 10° floor from April through September.
| Month | Fajr | Isha | Notes |
|---|---|---|---|
| Jan | 10.000° | 10.000° | Clipped; minimum night depth near 10° |
| Feb | 11.423° | 10.000° | |
| Mar | 11.355° | 10.000° | |
| Apr | 10.000° | 10.000° | Clipped both; perpetual civil twilight begins |
| May | 10.000° | 10.000° | Midnight sun conditions approaching |
| Jun | 10.000° | 10.000° | Midnight sun; no true night |
| Jul | 10.000° | 10.000° | |
| Aug | 10.000° | 10.000° | |
| Sep | 11.142° | 10.000° | Night recovering |
| Oct | 11.688° | 10.000° | |
| Nov | 10.345° | 10.000° | |
| Dec | 10.000° | 10.000° | Polar conditions; very short days |
MWL (18°) is unreachable for Fajr from approximately April through October. Any MWL Fajr times computed for Reykjavik during this period rely on fallback rules, not actual angle computation.
Glasgow, UK — 55.86°N, 4.26°W — elevation 18 m
Glasgow's strong seasonal variation makes it a challenging case for fixed methods. The Birmingham OpenFajr validation set (Glasgow, 95 records, MAE 0.52°) closely tracks these DPC predictions.
| Month | Fajr | Isha | Notes |
|---|---|---|---|
| Jan | 13.397° | 12.333° | Both methods within ~3° of MWL/ISNA |
| Feb | 14.234° | 12.552° | |
| Mar | 13.988° | 11.831° | |
| Apr | 13.172° | 10.000° | Isha begins to clip |
| May | 11.029° | 10.000° | Fajr drops sharply |
| Jun | 10.000° | 10.000° | Near-midnight sun; no valid Isha |
| Jul | 10.187° | 10.000° | |
| Aug | 12.541° | 10.000° | |
| Sep | 13.916° | 11.108° | |
| Oct | 14.439° | 12.481° | Autumn convergence |
| Nov | 13.744° | 12.519° | |
| Dec | 12.939° | 12.423° |
MWL (18°) would be 4–6° above the DPC Fajr angle in summer — representing 25–45 minutes of systematic error.
London, UK — 51.51°N, 0.13°W — elevation 5 m
London is the latitude band best supported by empirical data (OpenFajr London validation: 180 records, MAE 0.44°).
| Month | Fajr | Isha | Notes |
|---|---|---|---|
| Jan | 14.747° | 13.849° | |
| Feb | 15.605° | 13.738° | Peak winter Fajr angle |
| Mar | 15.272° | 13.020° | |
| Apr | 14.596° | 10.889° | |
| May | 12.892° | 10.000° | Isha clips |
| Jun | 11.796° | 10.000° | |
| Jul | 12.334° | 10.000° | |
| Aug | 14.047° | 10.000° | |
| Sep | 15.124° | 12.254° | |
| Oct | 15.606° | 13.744° | Seasonal peak |
| Nov | 15.122° | 13.904° | |
| Dec | 14.571° | 14.131° |
ISNA (15°) and London DPC are within 1° for most of the year — the reason ISNA works well in the UK. In June, the DPC angle is 11.8° vs ISNA's 15°, producing ~20 minutes difference.
Mediterranean & Middle East
Istanbul, Turkey — 41.01°N, 28.98°E — elevation 100 m
| Month | Fajr | Isha | Notes |
|---|---|---|---|
| Jan | 17.470° | 16.552° | |
| Feb | 17.995° | 16.298° | |
| Mar | 17.751° | 15.539° | |
| Apr | 17.466° | 13.658° | |
| May | 16.428° | 12.063° | |
| Jun | 16.083° | 12.289° | Minimum; Isha remains valid |
| Jul | 16.240° | 12.178° | |
| Aug | 17.253° | 12.884° | |
| Sep | 17.728° | 14.868° | |
| Oct | 18.086° | 16.203° | Approaches MWL Fajr range |
| Nov | 17.890° | 16.590° | |
| Dec | 17.498° | 16.955° |
Istanbul's DPC Fajr averages ~17.2° — below the MWL 18° standard but close. The Turkish Diyanet uses 18°/17° (DIBT), which closely tracks DPC here.
Cairo, Egypt — 30.04°N, 31.24°E — elevation 23 m
| Month | Fajr | Isha | Notes |
|---|---|---|---|
| Jan | 19.031° | 18.191° | |
| Feb | 19.624° | 18.112° | |
| Mar | 19.394° | 17.469° | |
| Apr | 19.164° | 15.979° | |
| May | 18.616° | 14.507° | |
| Jun | 18.603° | 14.827° | |
| Jul | 18.594° | 14.663° | |
| Aug | 19.227° | 15.213° | |
| Sep | 19.489° | 16.974° | |
| Oct | 19.694° | 17.963° | |
| Nov | 19.409° | 18.347° | |
| Dec | 18.960° | 18.545° |
Egypt's DPC Fajr averages ~19.2° — the Egyptian standard (19.5°) is a close match. This confirms that the Egypt method was calibrated for this latitude band.
Mecca, Saudi Arabia — 21.39°N, 39.86°E — elevation 270 m
| Month | Fajr | Isha | Notes |
|---|---|---|---|
| Jan | 19.650° | 18.978° | |
| Feb | 20.213° | 19.056° | |
| Mar | 20.260° | 18.870° | Peak Fajr angle |
| Apr | 20.065° | 17.646° | |
| May | 19.687° | 16.244° | |
| Jun | 19.630° | 16.387° | |
| Jul | 19.642° | 16.307° | |
| Aug | 20.083° | 16.884° | |
| Sep | 20.210° | 18.382° | |
| Oct | 20.286° | 19.122° | Highest Fajr |
| Nov | 20.016° | 19.109° | |
| Dec | 19.611° | 19.169° |
At Mecca, DPC Fajr averages ~19.9°. The higher DPC values (~20°) suggest Umm al-Qura's 18.5° may set Fajr slightly late.
South Asia
Islamabad, Pakistan — 33.68°N, 73.05°E — elevation 508 m
| Month | Fajr | Isha | Notes |
|---|---|---|---|
| Jan | 18.866° | 18.057° | |
| Feb | 19.280° | 17.826° | |
| Mar | 19.040° | 16.991° | |
| Apr | 18.883° | 15.487° | |
| May | 18.309° | 13.973° | |
| Jun | 18.117° | 14.183° | |
| Jul | 18.195° | 14.073° | |
| Aug | 18.862° | 14.716° | |
| Sep | 19.099° | 16.497° | |
| Oct | 19.354° | 17.690° | |
| Nov | 19.050° | 18.027° | |
| Dec | 18.774° | 18.374° |
The Karachi method (18°/18°) is widely used in Pakistan. DPC Fajr averages ~18.8° — the Karachi Fajr angle of 18° is slightly low.
Dhaka, Bangladesh — 23.81°N, 90.41°E — elevation 8 m
| Month | Fajr | Isha | Notes |
|---|---|---|---|
| Jan | 19.410° | 18.748° | |
| Feb | 19.977° | 18.839° | |
| Mar | 20.005° | 18.415° | |
| Apr | 19.746° | 16.956° | |
| May | 19.282° | 15.746° | |
| Jun | 19.340° | 16.032° | |
| Jul | 19.203° | 15.786° | |
| Aug | 19.728° | 16.406° | |
| Sep | 19.937° | 17.924° | |
| Oct | 20.048° | 18.676° | |
| Nov | 19.778° | 18.885° | |
| Dec | 19.365° | 18.929° |
DPC Fajr for Dhaka averages ~19.7°. The MUIS standard (20°) is a closer match to DPC here than Karachi (18°).
Southeast Asia & Oceania
Jakarta, Indonesia — 6.21°S, 106.85°E — elevation 8 m
Near the equator, seasonal variation is small but measurable.
| Month | Fajr | Isha | Notes |
|---|---|---|---|
| Jan | 18.893° | 17.989° | |
| Feb | 19.607° | 18.649° | |
| Mar | 19.936° | 19.440° | |
| Apr | 19.753° | 19.507° | Highest Isha of year |
| May | 19.264° | 19.028° | |
| Jun | 18.736° | 18.736° | Minimum |
| Jul | 18.989° | 18.756° | |
| Aug | 19.780° | 19.295° | |
| Sep | 20.053° | 19.556° | Highest Fajr of year |
| Oct | 20.007° | 19.277° | |
| Nov | 19.296° | 18.145° | |
| Dec | 18.828° | 17.721° |
DPC Fajr for Jakarta averages ~19.5°. The MUIS standard (20°) is close.
Melbourne, Australia — 37.81°S, 144.96°E — elevation 32 m
Southern Hemisphere: seasons are inverted. Melbourne summer = December/January; Melbourne winter = June/July.
| Month | Fajr | Isha | Notes |
|---|---|---|---|
| Jan | 17.013° | 12.803° | Southern summer |
| Feb | 18.045° | 13.615° | |
| Mar | 18.310° | 15.466° | Autumn transition |
| Apr | 18.545° | 16.768° | |
| May | 18.238° | 17.073° | |
| Jun | 17.994° | 17.615° | Southern winter |
| Jul | 18.109° | 17.151° | |
| Aug | 18.570° | 16.994° | |
| Sep | 18.444° | 16.111° | Spring transition |
| Oct | 18.249° | 14.498° | |
| Nov | 17.452° | 13.004° | |
| Dec | 17.037° | 13.111° |
Melbourne's DPC Fajr averages ~18.1°, making MWL (18°) a reasonable fit for the annual average.
Africa
Nairobi, Kenya — 1.29°S, 36.82°E — elevation 1,795 m
Near the equator but at high elevation (1,795 m), Nairobi's pressure correction affects the refraction term slightly.
| Month | Fajr | Isha | Notes |
|---|---|---|---|
| Jan | 18.841° | 18.611° | |
| Feb | 19.705° | 19.463° | |
| Mar | 20.207° | 19.957° | Both near maximum |
| Apr | 19.964° | 19.718° | |
| May | 19.206° | 18.971° | |
| Jun | 18.673° | 18.673° | Minimum |
| Jul | 18.928° | 18.697° | |
| Aug | 19.733° | 19.491° | |
| Sep | 20.049° | 20.049° | Maximum; very high |
| Oct | 20.077° | 19.831° | |
| Nov | 19.218° | 18.984° | |
| Dec | 18.582° | 18.355° |
Nairobi shows some of the highest DPC Fajr values (up to 20.2°). MWL at 18° would place Fajr 1.5–2° early on average. MUIS (20°) is a close match for most of the year.
Southern Hemisphere
Johannesburg, South Africa — 26.20°S, 28.05°E — elevation 1,753 m
| Month | Fajr | Isha | Notes |
|---|---|---|---|
| Jan | 19.440° | 15.760° | Southern summer |
| Feb | 19.960° | 16.485° | |
| Mar | 20.107° | 17.912° | |
| Apr | 20.186° | 18.841° | |
| May | 19.960° | 19.083° | |
| Jun | 19.623° | 19.195° | Southern winter |
| Jul | 19.675° | 19.026° | |
| Aug | 20.233° | 18.896° | |
| Sep | 20.349° | 18.566° | Highest Fajr |
| Oct | 20.328° | 17.164° | |
| Nov | 19.644° | 15.829° | |
| Dec | 19.497° | 15.963° |
Johannesburg's DPC Fajr averages ~19.9° — the Egypt method (19.5°) is a reasonable proxy.
What the patterns show
Several global patterns emerge from these 12 cities:
1. Latitude drives seasonal variation
Cities above 40° latitude (Istanbul, London, Glasgow, Reykjavik) show dramatic month-to-month angle swings — up to 5–6° for Fajr and even larger for Isha. Cities near the equator (Jakarta, Nairobi) show much smaller variation, typically 1–2° across the year.
2. Tropical cities have higher angles
Cities between 25°S and 25°N consistently produce DPC Fajr angles in the 19–20° range. The 35–45°N band averages 17–18°. High latitudes (50°N+) average 13–15°. This means:
- The MWL standard (18°) is a reasonable fit for mid-latitudes but too low for the tropics
- The MUIS standard (20°) is well-calibrated for Southeast Asia and equatorial Africa
- Neither standard is adequate for 50°N+ in summer
3. DPC and MSC are nearly identical
In all tables above, if you were to compute the MSC column it would differ from DPC by less than 5 minutes for most dates. Both methods track the same underlying physics — the difference is that DPC applies the Earth-Sun distance correction and smooth Fourier harmonics on top of the MSC seasonal base.
4. Fixed methods are appropriate for narrow latitude and season ranges
The Egypt method (19.5°) was calibrated for Cairo (30°N) and performs well there year-round. If you apply it to London (51.5°N), the summer error exceeds 30 minutes. Each method is only truly accurate for the latitude band and season it was calibrated against.
5. These are computed values, not empirically verified angles for each city
The Birmingham-latitude band (London, Glasgow) is the only region with empirical validation in the DPC training data. The Southern Hemisphere and tropical values are physics-based extrapolations. Where available, local Islamic authorities' established standards (validated by regional observation) should take precedence over DPC for official scheduling.