This document is part of my discussion of the Decline of the Lifespans of the Númenóreans. Please cite this essay if you quote it or use it. You can e-mail me.

Estimating the Lifespans of the Númenórean Kings

This is a simple way to estimate the lives of the Númenórean Kings. The purpose of this exercise is to begin to estimate the lifespans of the Lords of Andúnië, and to try to shed some light on what Tolkien might have been doing when he set up his own tables as time went on.

Stating in column A, type in numbers 1 to 25. That’s the order of the kings: there were 25, excluding Anducal, the usurper.

In column, B, put in the ages of the kings. You can look them up or take them from my earlier post.

In column C, put in 500 for the estimated age of the first king. Then put in 405 for kings 2 through 13. Beginning with king 14, take off 5.75% of the age of the previous king, and do that all the way to king 25. (The easiest way to do this is to multiply the estimated age of the king above by 0.9425, or 1 – 5.75%.)

Plot columns A, B, and C. If you use a line plot, A will become the x-axis. The data in Columns B and C line up very nicely.

If you want to see how much the estimate is off the actual, at the top of Column D (in cell D1), type in

=(c1-b1)/b1

That will give you the percent error of the estimate. Copy it into cells D2 to D25. Calculate the average (that is, =average(d1:d25) ), and you should get -0.29%.

This is very easy to do in a spreadsheet, but it’s very tedious to do by hand. That’s why I suggested Tolkien might have done this by graphing it. That way, he could just read the results off the graph, and of course, they’d always be just a little off the actual number. He didn’t have to use graph paper: if he was careful, he could have sketched it and gotten these results.

The average reign of a ruler should be same as the average time between generations. Elros was king longer than anyone else, and Vardamir was in fact never king at all (despite the “official” record that he reigned one year). For the next 11 kings, the average reign is 160 years, and so is the average length of time between generations. If you start with birth of Vardamir and add 160 years, you can get a good estimate of the birth year of the next 11 kings.

Starting with Ancalimon, the 14^th king, the reign of each king begins to shorten. Because the preceding king (each person’s father) outlives him, the length of each reign falls faster than the lifespan of each king. You can approximate this rate using a decline of –6.25%. Doing this, you can continue to add reigns/generations to each birth year until you arrive at king 25, Pharazôn, and get an estimate of 3114 for his birth year. The year Tolkien used (in the version of the story I used to build the model) is 3118.

	King	age	est. age	age error	ruled	target reign	error reign	born	target birth	error birth	age father	sovereign	age to rule	target sov.	error sov.	Retired	died	target death	error death
1	Elros	500	500	0.00%				-58			119	32				442	442	442	0.00%
2	Vardamir	410	405	-1.22%				61	60		131	442				443	471
3	Amandil	411	405	-1.46%	148	160	8.11%	192	220		158	442	200	420	-4.98%	590	603	600	0.50%
4	Elendil	401	405	1.00%	150	160	6.67%	350	380		193	590	200	580	-1.69%	740	751	785	-4.53%
5	Meneldur	399	405	1.50%	143	160	11.89%	543	540	0.55%	157	740	200	740	0.00%	883	942	945	-0.32%
6	Aldarion	398	405	1.76%	192	160	-16.67%	700	700	0.00%	173	883	200	900	1.93%	1075	1098	1105	-0.64%
7	Ancalimë	412	405	-1.70%	205	160	-21.95%	873	860	1.49%	130	1075	200	1060	-1.40%	1280	1285	1265	1.56%
8	Anárion	401	405	1.00%	114	160	40.35%	1003	1020	-1.69%	171	1280	200	1220	-4.69%	1394	1404	1425	-1.50%
9	Súrion	400	405	1.25%	162	160	-1.23%	1174	1180	-0.51%	146	1394	200	1380	-1.00%	1556	1574	1585	-0.70%
10	Telperiën	411	405	-1.46%	175	160	-8.57%	1320	1340	-1.52%	154	1556	200	1540	-1.03%	1731	1731	1745	-0.81%
11	Minastir	399	405	1.50%	138	160	15.94%	1474	1500	-1.76%	160	1731	200	1700	-1.79%	1869	1873	1905	-1.71%
12	Ciryatan	401	405	1.00%	160	160	0.00%	1634	1660	-1.59%	166	1869	200	1860	-0.48%	2029	2035	2065	-1.47%
13	Atanamir	421	405	-3.80%	192	160	-16.67%	1800	1820	-1.11%	186	2029	189	2009	-1.01%		2221	2225	-0.18%
14	Ancalimon	400	382	-4.57%	165	150	-9.09%	1986	1970	0.81%	150	2221	178	2148	-3.30%		2386	2352	1.44%
15	Telemmaitë	390	360	-7.75%	140	141	0.45%	2136	2111	1.19%	141	2386	167	2278	-4.52%		2526	2470	2.20%
16	Vanimeldë	360	339	-5.81%	111	132	18.77%	2277	2242	1.52%	129	2526	158	2400	-4.98%		2637	2582	2.10%
17	Alcarin	331	320	-3.45%	100	124	23.60%	2406	2366	1.66%	110	2657	149	2515	-5.35%		2737	2686	1.88%
18	Calmacil	309	301	-2.52%	88	116	31.67%	2516	2482	1.35%	102	2737	140	2622	-4.20%		2825	2783	1.48%
19	Ardamin	281	284	1.03%	74	109	46.80%	2618	2591	1.05%	91	2825	132	2723	-3.62%		2899	2874	0.85%
20	Adûnakhôr	253	268	5.76%	63	102	61.65%	2709	2692	0.61%	89	2899	125	2817	-2.83%		2962	2960	0.07%
21	Zimrathôn	235	252	7.31%	71	95	34.47%	2798	2788	0.36%	78	2962	117	2905	-1.92%		3033	3040	-0.23%
22	Sakalthôr	226	238	5.17%	69	90	29.72%	2876	2877	-0.05%	84	3033	111	2988	-1.48%		3102	3115	-0.42%
23	Gimilzôr	217	224	3.23%	75	84	11.88%	2960	2961	-0.04%	75	3102	104	3066	-1.17%		3177	3185	-0.26%
24	Palantir	220	211	-4.03%	78	79	0.86%	3035	3040	-0.16%	83	3177	98	3138	-1.22%		3255	3251	0.12%
25	Pharazôn †	201	199	-1.00%	64	74	15.24%	3118	3114	0.14%		3255	93	3206	-1.50%		3319	3313	0.19%
	average			-0.29%			12.34%			0.11%					-2.27%				-0.02%

Now you can set a similar spreadsheet for the Lords of Andúnië. Substitute Silmariën for her brother Meneldur, and Valandil for his cousin Aldarion. You’ll need another column to count the Lords of Andúnië; Valandil is the first one. Knock out all the names until you get to the 15th lord: that’s Eärendur. The 16th lord is not named; the 17th is Numendil, the 18th Amandil, and the 19th would have been Elendil, who went to Middle-earth. You will notice that you have 2 fewer generations than in the line of the kings.

The goal here is to find the correct ratios of: (1) the shrinkage of the lifespans and (2) the length of the reigns; in order spread out the lines of the Lords of Andúnië to get a good estimate of the assigned birth-year for Elendil, 3119.

Non-sequitur: Just as Ar-Pharazôn is one year older Elendil, Denethor II is one year older than Aragorn. Perhaps that’s another bad-king/good-king pair, and perhaps this is more than coincidence; although I’m not sure Tolkien intended any such inference. I really don’t consider Denethor a wicked person by any means. Even if Tolkien intended such an inference – that is, Ar-Pharazôn: Elendil::Denethor:Aragorn – I have no idea how anyone could demonstrate that linkage without some explicit statement or reasonably clear discussion on the part of Tolkien himself. It’s just a non-sequitur.