Moon and astronomy
Crescent Visibility Criteria: How the Hilal Is Predicted
Crescent visibility criteria use moon age, lag, altitude and elongation to estimate if the hilal can be seen. See how Danjon, Yallop and Odeh compare.
By Tahir Nasuru · · 10 min read
A crescent visibility criterion is a rule, built from past sightings, that estimates whether the thin first crescent (the hilal) can be seen from a given place on a given evening. Old rules used only the Moon's age and its lag time after sunset. Modern criteria, such as those of Yallop (1997) and Odeh (2004), combine how far the Moon stands above the Sun with how wide the lit crescent is. Their answer is a likelihood category, from "easily visible" to "not visible", not a guarantee.
Key Takeaways
- The new moon can be calculated exactly. Whether the crescent will be seen can only be estimated.
- Moon age or lag time on its own is a poor predictor. Modern criteria pair the Moon's height above the Sun with the width of the crescent.
- The Danjon limit (about 7°, or 6.4° in Odeh's data) is the elongation below which no crescent has reliably been seen.
- Yallop's q-test and Odeh's V-test both sort an evening into zones; weather, haze and observer skill still decide the outcome.
Why visibility has to be predicted, not calculated
The US Naval Observatory's crescent visibility page separates two problems. The time of new moon is a geometric event and can be computed to the minute. Seeing the crescent depends on many factors and "cannot be predicted with certainty." The crescent usually becomes visible about a day after new moon, but USNO notes that the timing varies quite a bit from month to month.
The reason is that the eye has to pick a very faint, very thin arc out of a bright twilight sky, close to the horizon where the air dims it. Geometry, the atmosphere and human vision all play a part. That is also why, as R.H. van Gent of Utrecht University points out in his introduction to first-visibility prediction, planetarium software can show where the Moon is but cannot tell you whether it will be seen.
For Muslims this matters because the Quran calls the crescents (al-ahilla) markers of time for people and for Hajj (Quran 2:189). How communities use sightings and predictions to start a month is a separate question, covered in moon sighting vs calculation. This article only explains what the astronomical criteria measure.
The parameters every criterion uses
Each criterion is built from a few measurements taken at or just after sunset. In his paper on a new crescent visibility criterion (Experimental Astronomy 18, 2004), Mohammad Odeh lists the standard ones:
| Parameter | What it measures | What it tells you |
|---|---|---|
| Moon age | Time since the new moon (conjunction) | Rough guide only |
| Lag time | Minutes between sunset and moonset | How long the Moon stays up in twilight |
| Altitude | The Moon's height above the horizon | How much air the light passes through |
| Arc of light (ARCL), or elongation | Angle between the Sun and Moon | How wide and bright the crescent is |
| Arc of vision (ARCV) | Difference in altitude between Moon and Sun | How dark the sky is around the Moon |
| Relative azimuth (DAZ) | Sideways separation of Sun and Moon | Whether the Moon sits above or beside the sunset point |
| Crescent width (W) | Width of the lit part, in arc minutes | Direct measure of how much light there is |
ARCL, ARCV and DAZ are linked: if the Moon sits straight above the setting Sun, DAZ is zero and the arc of light equals the arc of vision. When the Moon is off to one side, it is lower in the sky for the same elongation.
Why age and lag are not enough
Age and lag time are the easiest numbers to quote, and the oldest. Odeh's paper summarises the Babylonian rule as: the crescent is visible if, at sunset, the Moon is more than 24 hours old and sets more than 48 minutes after the Sun.
The problem is that age is only loosely tied to brightness. The Moon can be anywhere from 0° to 5° from the Sun at the moment of new moon, according to USNO, and its speed along its orbit changes with distance. So after one day the elongation can range from roughly 10° to 15°. Two crescents of the same age can differ a lot in width. Odeh, citing earlier work by Schaefer, states that using age or lag alone "has no predicting value at all." USNO likewise calls elongation a more reliable starting point than age.
The Danjon limit: the hard floor
The Danjon limit is the smallest Sun-Moon separation at which a crescent can be seen at all. Below it, the lit arc becomes too short and too faint to register, even through a telescope.
According to Odeh's review, André Danjon reported in 1936 that no crescent can be seen when the Moon is less than 7° from the Sun. Later researchers proposed different values and explanations. Odeh's own database of 737 observations gave a limit of 6.4° with optical aid, and its smallest naked-eye elongation was 7.7°. Yallop's NAO Technical Note 69 adds that, in practice, it is rare to see the crescent below an apparent elongation of about 7.5°.
The Danjon limit is a necessary condition, not a sufficient one. Passing it only means a sighting is not ruled out.
Yallop's q-test
Bernard Yallop worked in the computing section of HM Nautical Almanac Office (HMNAO) in the UK. His 1997 method, published as NAO Technical Note 69, adapted earlier tables from Maunder (1911), the Indian Astronomical Ephemeris and Bruin (1977). He calibrated it against a standard list of 295 first-sighting records from 1859 to 1996, which includes failed attempts as well as successes.
The method works in three steps.
- Pick the best time to look. Yallop's rule is sunset plus four-ninths of the lag time. If the Moon sets 90 minutes after the Sun, the best time is 40 minutes after sunset. Earlier, the sky is too bright. Later, the Moon is too low and dimmed by the air.
- Measure two things at that moment. The arc of vision (ARCV) and the crescent width (W), worked out for the observer's position.
- Compute q. The q value is how far ARCV exceeds the minimum height needed for a crescent of that width, divided by ten so that it falls roughly between −1 and +1.
The result falls into one of six bands. The thresholds below are from Table 5 of the technical note, also listed on van Gent's page on Yallop's method.
| Code | q value | Meaning |
|---|---|---|
| A | above +0.216 | Easily visible to the naked eye |
| B | +0.216 to −0.014 | Visible to the naked eye under perfect conditions |
| C | −0.014 to −0.160 | May need optical aid to find the crescent first |
| D | −0.160 to −0.232 | Can only be seen with binoculars or a telescope |
| E | −0.232 to −0.293 | Below the normal limit for a telescope |
| F | below −0.293 | Not visible; below the Danjon limit |
Yallop was open about the limits. He found that a few sightings from very clear, high-altitude sites contradicted the test, and noted that the Moon's shallow path at high latitudes needs more observations to predict well.
Odeh's criterion
Mohammad Odeh, working with the Islamic Crescent Observation Project (ICOP), published a criterion in 2004 built on 737 observations, almost half of them gathered by ICOP members. It uses the same two ingredients as Yallop, the arc of vision and the crescent width, both measured from the observer's position. It gives a value V and four zones:
| Zone | V value | Meaning |
|---|---|---|
| A | 5.65 or more | Visible by naked eye |
| B | 2 to 5.65 | Visible with optical aid, and could be seen by naked eye |
| C | −0.96 to 2 | Visible with optical aid only |
| D | below −0.96 | Not visible even with optical aid |
Odeh adds a caution that applies to every criterion: visibility at the start of each zone depends heavily on atmospheric conditions, eyesight, experience and knowing where to look. An evening that only just enters zone C may produce no sighting at all if the sky is hazy.
A worked example: the start of Ramadan 1447
The evenings of 17 and 18 February 2026 show how the criteria behave. The new moon fell on 17 February at 12:01 UT. HM Nautical Almanac Office's crescent visibility guidance for February 2026 said no naked-eye sighting was likely anywhere on the 17th, and that most places could see the crescent easily on the 18th, with exceptions.
The figures below were computed for this article with the astronomy-engine library (Python, version 2.1.19), at sea level for Makkah (21.42° N, 39.83° E), London (51.51° N, 0.13° W), Jakarta (6.21° S, 106.85° E) and Cape Town (33.92° S, 18.42° E). Age, lag and the Moon's altitude (airless, as seen from the city) are at local sunset. ARCL, DAZ, q and V are at Yallop's best time: geocentric ARCV, DAZ and ARCL for q, and topocentric airless values for V, as each paper specifies. Treat the q and V values as illustrations; they can differ slightly from HMNAO's or ICOP's own software. The last column quotes HMNAO's summary for February 2026: its table for Makkah and London, and its notes for Jakarta and Cape Town.
| City (18 Feb 2026) | Age at sunset | Lag | Moon altitude at sunset | ARCL | DAZ | Yallop q | Odeh V | HMNAO summary |
|---|---|---|---|---|---|---|---|---|
| Makkah | 27.3 h | 59 min | 12.2° | 14.2° | 0.5° | +0.53 (A) | 8.6 (A) | "Easily Visible" |
| London | 29.3 h | 86 min | 11.2° | 15.4° | 7.3° | +0.51 (A) | 8.5 (A) | "Easily Visible" |
| Jakarta | 23.2 h | 40 min | 8.7° | 12.0° | 5.9° | +0.08 (B) | 4.2 (B) | "may be visible under excellent conditions" |
| Cape Town | 29.6 h | 35 min | 6.3° | 15.3° | 13.1° | −0.05 (C) | 3.0 (B) | "optical aid may be required to sight the crescent moon" |
Three things stand out.
- Age misleads. Cape Town's Moon was older than Makkah's, yet harder to see. It stood about 13° to the side of the sunset point, so it was lower and set only 35 minutes after the Sun.
- The old rule fails at the edges. Jakarta's Moon was under 24 hours old with a 40-minute lag, so the Babylonian rule says "not visible". Yallop's test puts it in B (visible under perfect conditions), and HMNAO's note says it may be visible under excellent conditions.
- Criteria can disagree. For Cape Town, Yallop's q puts the evening in C (optical aid needed to find it) while Odeh's V puts it in B (could be seen by naked eye). Near the boundaries, the choice of criterion changes the label.
On 17 February the Moon set before the Sun in Jakarta and only a few minutes after it in Makkah, London and Cape Town, with q values near −1: category F everywhere in the table.
The calculated Umm al-Qura calendar used on this site shows 1 Ramadan 1447 as 18 February 2026, which as an Islamic day began at sunset on the 17th. That calendar follows its own rule, not a visibility criterion, as explained in the Umm al-Qura calendar explained. Communities that waited for a sighting could reach a different start date.
What a prediction can and cannot tell you
A visibility map or table answers one question: given the geometry, how likely is it that a careful observer in clear air could see the crescent? It cannot know whether there will be cloud, dust or haze on the night, whether the observer has good eyesight, or whether they look in the right place at the right time.
The records show how much those factors matter. USNO reports the youngest reliable naked-eye sighting at about 15.5 hours after new moon, and 12.1 hours with a telescope. Odeh's database lists a naked-eye sighting at 15 hours 33 minutes (measured from the observer's position) and a shortest naked-eye lag of 29 minutes. These are exceptional cases under excellent conditions. A typical evening needs a much older, higher crescent.
So a forecast is best read as a probability band. "Easily visible" means a sighting is expected if the sky is clear. "Optical aid needed" means most people will not see it without help. "Not visible" means a claimed sighting would conflict with the criterion. How a sighting committee weighs such a claim is a matter for that body and its scholars, not for the criterion. For a step-by-step guide to the numbers on a forecast page, see how to read a crescent moon forecast.
What to do next
Before the start of an important month, check the next new moon on the moon phases page. Then look at an official visibility forecast, such as HMNAO's monthly guidance, for your region on the following one or two evenings. If you plan to look yourself, go out near the best time, about four-ninths of the way from sunset to moonset, and scan low in the west just above the sunset point.
For dates, use the date converter or the Ramadan page as a calculated planning estimate, and confirm the start of the month with the local authority or mosque you follow.
