pray-calc/.github/wiki/Asr-Calculation.md

Asr Calculation

The Rule

Asr is the afternoon prayer. Its start time is defined by shadow length, not by a solar depression angle.

The standard definition: Asr begins when an object's shadow equals its height plus the length of its shadow at solar noon.

For the Shafi'i, Maliki, and Hanbali schools of law (the majority), the shadow multiplier is 1. For the Hanafi school, the multiplier is 2.

In practice, the difference is typically 30–60 minutes, with Hanafi Asr being later.

The Math

Let:

• φ = observer latitude in radians
• δ = solar declination in radians at local noon
• s = shadow factor (1 for Shafi'i, 2 for Hanafi)

The Sun's altitude when the shadow multiplier condition is met:

A = arccot(s + tan(|φ - δ|))
  = arctan(1 / (s + tan(|φ - δ|)))

This altitude corresponds to a specific hour angle H:

cos(H) = (sin(A) - sin(φ)sin(δ)) / (cos(φ)cos(δ))

Asr time in local fractional hours:

asrTime = solarNoon + H / 15  (H in degrees, since 15° = 1 hour)

If cos(H) < -1 or cos(H) > 1, the Sun never reaches the required altitude, and getAsr returns NaN. This can happen at extreme latitudes when latitude and declination are far apart.

Implementation

getAsr is a pure math function. It requires:

1. solarNoon: fractional hours (from the SPA output)
2. latitude: decimal degrees
3. declination: solar declination in degrees (from solarEphemeris)
4. hanafi: boolean (default false)

import { getAsr } from 'pray-calc';

const asr = getAsr(
  12.15, // solar noon at ~12:09 local time
  40.7128, // New York latitude
  23.44, // solar declination at summer solstice
  false, // Shafi'i
);

Why Not Use the SPA for Asr?

Some prayer time libraries solve for Asr by running the SPA with the altitude A as the zenith input. This requires an extra SPA call or a second zenith slot in the batch call.

pray-calc computes Asr analytically using the Meeus declination (solarEphemeris) rather than the SPA's internal declination. This avoids a second SPA call, removes any dependency on internal SPA state, and is accurate to well within a minute for any realistic use case.

The SPA uses a more rigorous ephemeris for declination (accurate to ~0.0003° vs. Meeus at ~0.01°). For Asr, the difference in δ of 0.01° translates to less than 5 seconds of timing error: completely negligible.

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