Robustness

Don't pick a model. Run all of them.

Every tool that dates the crucifixion picks one reconstruction and reports the dates it produces. But the reconstruction involves at least four choices nobody can settle, and each one moves the answer. So rather than choose, this page runs the whole space and counts how often each year survives.

Read this before the numbers. What follows is a sensitivity analysis, not a probability. A year scoring 54.5% does not mean there is a 54.5% chance the crucifixion happened then. It means: across the defensible ways of reconstructing the Hebrew calendar, that fraction of them put Nisan 14 on a Friday that year. It measures how much the answer depends on assumptions — nothing more. Treating it as a historical probability would be exactly the false precision this site exists to refuse.

What gets varied

The visibility criterion

A month begins when the crescent is first seen. Three ways to model that: a flat moon-age cutoff, Yallop's q (1997), and Odeh's V (2004). The latter two use real crescent width and altitude geometry; the first is the crude proxy most popular accounts amount to.

The moon-age threshold

If you use the crude proxy, how old must the moon be at sunset — 20 hours? 28? Every value in that range has been defended, and the choice moves dates by a full day.

Which lunation is Nisan

Full moon after the equinox, new moon after the equinox, or Stern's finding that first-century practice ran late and Passover always followed the equinox. These can differ by an entire month.

ΔT

The dynamical-to-universal time correction is about 2.86 hours at this epoch, extrapolated from sparse eclipse records. We vary it by ±10 minutes, which is conservative.

The sweep

Which day

Target weekday

From (AD)

To (AD)

Showing the default sweep, computed when this page was built. Change anything above and it recomputes in your browser — nothing is sent anywhere.

AD 2754.5%

AD 3048.5%

AD 3330.3%

AD 3410.1%

Year	Models surviving	Share	Date(s) produced
AD 27	54 / 99	54.5%	11/4 (54)
AD 30	48 / 99	48.5%	7/4 (48)
AD 33	30 / 99	30.3%	3/4 (30)
AD 34	10 / 99	10.1%	23/4 (10)

How to read this

Run it on the defaults and the ranking is not the one you would expect from popular accounts: the year surviving the most models is AD 27, not AD 30 or AD 33. That result stood on this page for some time. It is an artifact, and the section below shows how we caught it.

What the sweep does establish survives the correction, and is the point worth keeping: the calendar alone does not single out a year. The narrowing to AD 30 and AD 33 is done with non-calendrical evidence — the length of the ministry, John the Baptist beginning in the fifteenth year of Tiberius, the tenure of Pilate. Those are historical arguments, and no ephemeris adjudicates them.

The limits of this page. The space swept here is the space this software implements — three criteria, three Nisan rules, one range of ΔT error. It is not every model a scholar might defend, and the weights are uniform. A different space would give different percentages. The robust finding is the spread, not the decimals.

Which criterion is actually any good?

Weighting every model equally is a confession, not a method. It says we have no reason to prefer one crescent rule over another. But a visibility criterion is a falsifiable predictor — give it a date and a place and it says the month begins tonight or it doesn't — so it can be scored against calendars that have nothing to do with this question at all.

Parker & Dubberstein tabulate 8,670 Babylonian month beginnings from 626 BC – AD 76: the standard reference chronology for the period. Running each criterion at Babylon across that span gives a hit rate that no amount of argument can talk around.

Criterion	Agrees with P&D	Months differing	Mean error
Odeh V, band A	94.99%	434 / 8,670	+0.022 d
Yallop q, bands A–B	91.97%	696 / 8,670	-0.059 d
Yallop q, band A	89.17%	939 / 8,670	+0.102 d
Moon age ≥ 20 h	82.95%	1,478 / 8,670	-0.067 d
Moon age ≥ 22 h	82.63%	1,506 / 8,670	+0.011 d
Yallop q, bands A–C	82.51%	1,516 / 8,670	-0.167 d
Moon age ≥ 24 h	79.27%	1,797 / 8,670	+0.098 d
Odeh V, bands A–B	75.03%	2,165 / 8,670	-0.246 d
Moon age ≥ 26 h	74.68%	2,195 / 8,670	+0.185 d
Moon age ≥ 28 h	69.20%	2,670 / 8,670	+0.267 d
Odeh V, bands A–C	51.95%	4,166 / 8,670	-0.480 d

Yallop's criterion tracks the reference chronology far better than any flat moon-age cutoff — and the 24-hour cutoff that popular reconstructions lean on, the one this site's own frozen core uses, is wrong about one month in five.

Is the astronomy here trustworthy at all? An outside check.

R. H. van Gent (Utrecht) ran essentially this comparison independently — modern lunar theory plus Yallop, against Parker & Dubberstein — and reports 680 of 8,670 lunations differing, or 7.84%. This site's engine, which he has never seen, gets 696 — 8.03%. The residual is what you would expect from using Meeus's abridged series where he uses full ELP/VSOP theory.

That agreement is the best evidence available that the lunar positions, ΔT, sunset solver and visibility maths on this site are right — corroborated end to end by someone with no connection to it.

What this does not show. Parker & Dubberstein's month-starts are themselves mostly computed — from Carl Schoch's 1928 visibility algorithm, corrected against cuneiform attestations where those survive. So the table above measures agreement with the standard reconstruction, not with what an observer in Babylon actually saw. Scoring well earns a criterion more weight than a rival; it does not establish that first-century Judea used it, and Judea is not Babylon. The honest gain is narrower than it looks: we have moved from no reason to prefer a criterion to one reason, and it is a reason about reconstructions rather than observations.

The sources behind these tables →

What the measurement changed

Once each configuration has a score, the sweep can be interrogated instead of just averaged. Two things fell out, and both change what this page previously claimed.

The most sensitive assumption was the one nobody varied

Yallop and Odeh return a graded index, not a yes or no. Turning that into a calendar decision needs a cutoff — which band still counts as "the month begins" — and their papers do not settle it, because the bands describe how hard the crescent is to see, not when a community declared a new month. This software hardcoded that cutoff for years without saying so.

Measured against Parker & Dubberstein, moving the cutoff swings agreement from 51.95% to 94.99%. That is a wider spread than the visibility criterion, the moon-age threshold, the Nisan rule and ΔT put together. The most load-bearing assumption in the model was invisible. It is now a swept parameter like the rest.

AD 27 was an artifact of the crudest criterion

Splitting the sweep by criterion instead of averaging over it:

Criterion	Agreement with P&D	Configurations yielding AD 27
Flat moon-age cutoff	69–83%	100%
Yallop q	83–92%	33%
Odeh V	52–95%	0%

AD 27 is unanimous under the flat moon-age cutoff, a minority result under Yallop, and never appears at all under Odeh. The flat cutoff is also the worst performer against the reference chronology — and because it carries a tunable threshold, it occupied 45 of the 99 combinations swept. The least accurate criterion both dominated the space and unanimously favoured one year. That is where "AD 27 is the most robust year" came from.

What the best-evidenced configurations give

Restricting to configurations that agree with P&D at 89% or better — yallop:A, yallop:AB, odeh:A — and holding the Nisan rule fixed rather than averaging across mutually exclusive scholarly positions. The gospel chronology is held fixed too, and shown as a column, because it is a choice and not a constant:

Nisan rule	14 Nisan — John	15 Nisan — Synoptics
Full moon on or after the equinox	AD 30 (100%), AD 33 (100%), AD 27 (33%)	AD 27 (67%)
New moon on or after the equinox	AD 27 (33%)	AD 34 (100%), AD 27 (67%)
Passover strictly after the equinox (Stern)	AD 30 (100%), AD 27 (33%)	AD 34 (100%), AD 27 (67%)

Read the left column and the familiar result appears: under the two Nisan rules most scholars actually hold, the best-evidenced configurations converge on Friday 7 April AD 30 and Friday 3 April AD 33, unanimously and with no tuning — precisely the two dates the scholarship argues over.

Now read the right column. This page previously printed the left one alone, and stated its conclusion without the condition. Under the synoptic chronology — 15 Nisan, the reading three of the four gospels support on their surface — the same best-evidenced machinery returns entirely different years, and neither AD 30 nor AD 33 appears at all. The site offers 14-or-15 as a control on two pages and calls the disagreement "part of the evidence rather than something to be tidied away", then held it fixed for the one table that stated a conclusion. That was the hardcoded band cutoff wearing a different hat: ΔT was being swept by ten minutes while the most disputed textual parameter in the whole debate sat pinned at one value. The correct statement of the result carries its condition: if John's chronology is right, the best-evidenced models give AD 30 and AD 33.

Read this before concluding anything. This is not a demonstration that the crucifixion happened in AD 30 or AD 33. Four limits, all of them real. One: two years survive, not one — the calendar still fails to single out a year, which was this page's original point and remains its soundest. Two: the result is conditional on John's chronology, as the table above now shows. Three: the weighting rests on agreement with Parker & Dubberstein, whose month-starts are themselves mostly computed from Schoch's 1928 criterion; a configuration that tracks it has matched a reconstruction, not an observation. Four: Babylon is not Jerusalem, and a criterion that models clear-sky visibility models neither cloud nor the Sanhedrin's requirement that two witnesses actually come forward. The gain here is narrow and specific: two claims this page used to make have been shown to depend on hidden parameters, and both parameters are now visible.

The argument that says this whole page is misconceived

Every objection above is an objection to one of this page's inputs. There is a published objection to its premise, and it is the strongest thing written against what this site does.

Helen Bond ("'Dating the Death of Jesus': Memory and the Religious Imagination", New Testament Studies 59.4 (2013), 461–475) does not propose a rival year. She argues the question is not answerable at the resolution everyone is working at. Her conclusion: “the precise date can no longer be recovered. All we can claim with any degree of historical certainty is that Jesus died some time around Passover (perhaps a week or so before the feast) between 29 and 34 CE”.

What she keeps

The Friday, and the Thursday evening meal. Both traditions agree Jesus was crucified on a Friday and buried that afternoon, and she uses the agreed Thursday supper to reject Jaubert's Tuesday and Humphreys's Wednesday reconstructions — solving one discrepancy by creating another, as she puts it.

What she removes

The assumption that the Friday was 14 or 15 Nisan. In Mark only two passages tie the supper to Passover — 14:1a, a Markan double time reference, and 14:12–16, modelled on the colt story of 11:1–11 — and both are widely held to be redactional. Strip them and nothing in Mark's passion narrative links the death to the feast. She adds that Mark 14:2 has the priests deciding not to arrest during the festival.

So her position is testable with this page's own engine: keep the Friday, drop the fixed Nisan day, and ask which years in AD 29–34 contain a Friday in the fortnight before Passover.

Year	Candidate Fridays before Passover
AD 29	8/4 (Nisan 4), 15/4 (Nisan 11)
AD 30	31/3 (Nisan 7), 7/4 (Nisan 14)
AD 31	16/3 (Nisan 3), 23/3 (Nisan 10)
AD 32	4/4 (Nisan 5), 11/4 (Nisan 12)
AD 33	27/3 (Nisan 7), 3/4 (Nisan 14)
AD 34	12/3 (Nisan 2), 19/3 (Nisan 9)

6 of 6 years qualify, with 12 candidate dates between them. The discriminating power of the astronomy is 0.00. Under Bond's reading this page does not narrow the field at all — not to two years, not to four, but to every year in the range. That is her argument, and running it through this site's own machinery does not weaken it. It is the honest answer to "what if the premise is wrong": then everything above is a precise answer to a question the sources cannot support.

And she independently corroborates the astronomy

In passing, Bond reports that under the synoptic dating "Nisan 15 fell on a Friday only in 27 CE and 34 CE". This engine, which she has never seen, returns AD 27 and AD 34 — exactly her pair. That is an external check of the same kind as van Gent's on the Babylonian months, and it is worth just as much.

With one honest qualification. The match is on the union across Nisan rules. Under the commonest single rule this engine returns AD 27 alone; AD 34 appears under the other two. So the agreement is real but not rule-for-rule, and stating it without that caveat would be overclaiming.

Nothing on this page answers her. The candidates above are computed correctly, and if the death was not on a fixed Nisan day then computing them correctly was never the difficulty. Readers should weigh that before treating any year on this site as an answer.

The non-calendrical arguments, enumerated the same way → · Where Bond sits among the other scholars →

How each of these models is computed →