Readers of Tolkien know well that in battle scenes, he gives little information about the size of the armies involved. One case is with the Battle of Five Armies, as described in ‘The Hobbit’. In this analysis I shall lay out all findings regarding this battle, focusing on the statistics; and using both the obvious and the known found in quotes and information from Tolkien’s:-

The Hobbit
The Lord of the Rings: The Return of the King – Appendices A and B.
Unfinished Tales – The Quest of Erebor

And from:
The History of the Hobbit’ (Volume 1) by John D Rateliffe
The Atlas of Middle Earth by Karen Wynne Fonstadt

The battle itself is described in The Hobbit; Ch. 17; The Clouds Burst but in previous and succeeding chapters we find hints and information about all armies involved. There is no question that from its name, we can make out that the five armies involved are: elves, dwarves, men, goblins and wargs. (plus a small force of eagles – to whom I refer later on).

Ch. 14: Fire and Water.
In this chapter, during Smaug’s attack on Lake-Town, we are presented with the following:
“… every warrior was armed, every arrow and dart was ready.”
“… a hail of dark arrows leaped up and snapped and rattled on his scales and jewels …”
“… cheering on the archers” (Bard)
“… there was still a company of archers.”

So there is no doubt that Lake-Town had some form of army as words like ‘warrior’, ‘archers’ and ‘company’ are clear references.

We are not told numbers at this point so we can only guess. A few hundred would have certainly been present because although many had died or fled during the town’s destruction, some remained to fight the Battle alongside the Elves.

In the same chapter, after the death of Smaug, , we are told about the Wood Elves’ army coming to the men’s rescue. “He [the Elvenking] had not boats or rafts enough for his host, and they were forced to go the slower way by foot.” The word “host” here implies quite a large number of people. In fact, the dictionary describes ‘host’ as ‘a great multitude, a muster’ – just like the mustering of Rohan at the time of the War of the Ring.

It can be assumed that in order to help the men of Lake-Town, and carry the large supplies we are told of in the book, the Elvenking would have needed as many elves as he could gather.
“… elves are lightfooted, and though they were not in those days much used to the marches and the treacherous land between the Forest and the Lake, their going was swift. Only five days after the death of the dragon they came upon the shores and looked on the ruins of the town.” Which seems to mean that although the Elves were in a large number, they still managed to arrive at the Lake fairly quickly.
“… all the men of arms who were still able, and the most of the Elvenking’s array, got ready to march …”

So now we know that the men who had survived the attack on Lake-Town and the majority of the Elf army headed towards the Mountain and once again ‘array’ is used to describe the Elven force.

Ch. 15: The Gathering of the Clouds.
“… many are gathering hither beside the birds … Already a host of the elves is on the way …” (Roäc to Thorin).
Again the word ‘host’ is used along with the word ‘many’. I do not know what Tolkien actually meant by ‘many’ but I think that, because this was specifically a children’s book, it would not have implied a vast force comparable to, say, the ones at Helm’s Deep or the Pelennor Fields in ‘The Lord of the Rings’.
“There came a night when suddenly there were many lights as of fires and torches away south in Dale before them.”
“ ‘They have come!’ said Balin. ‘And their camp is very great.’ ”

The term ‘many’ is used again, and linked to the previous quote, reinforces the idea of a large force.

Ch16: A Thief in the Night
This chapter contains only one relevant quote and it is, ironically, one of only two in all ‘The Hobbit’ book, that gives any reference to any army’s numbers.
“… ravens brought news that Dáin and more than five hundred dwarves, hurrying from the Iron Hills, were now within about two days’ march of Dale …”
Most readers are aware of the idea that five hundred dwarves participated in the Battle of Five Armies, but ‘more than’ leaves it still unclear. How much more than that figure they could be is impossible to state, but what is definitive is that (including Thorin, his company, Dáin and the other Dwarves, between 550 and 600 were present that day of the battle.

Ch. 17: The Clouds Burst
In this chapter the main battle takes place and we have the second reference to army numbers.
“About midday the banners of the Forest and the Lake were seen to be born forth again. A company of twenty was approaching.”
“ ‘…we will depart, and the elf-host will go back to the Forest.’ ” (Bard to Thorin)

Here again the words ‘company’ and ‘host’ are used to reinforce the idea of a large army. Although the company mentioned above was said to contain only twenty people, this word signifies different sizes as we will see in the next quote.

“Bard, of course, refused to allow the dwarves to go straight on to the Mountain … if once the fortress was manned with so large and warlike a company.” So here, unlike the above quote, ‘company’ clearly refers to the five hundred dwarves that have arrived to help Thorin and his companions, this group being referred to as ‘large’. If such a number is considered ‘large’, what of the Elven army which (as we shall see later) comprises many more than the Dwarves? Would they be considered a “host”?

In this chapter, we are also told that the Elven army (always giving reference to the Men of Lake-Town too) could mount a siege:
“They [the Dwarves and Dáin] would stand a siege for weeks.”
“Also they would be able to reopen and guard some other gate, so that the besiegers would have to encircle the whole mountain; and for that they had not sufficient numbers.”

Returning to the issue of the ‘large’ force of Dwarves, the Elvenking makes the following statement:
“‘Our advantage in numbers will be enough if in the end it must come to unhappy blows.’”
It is clear then that the Elven army is a much superior force than that of the Dwarves although exact numbers are, as yet, still uncertain.

For a moment, let us leave the Elves, Dwarves and Men for a while and focus on the Wargs and Goblins. As they approach, Gandalf burst out shouting:
“Behold! The bats are above this [Bolg’s] army like a sea of locusts. They ride upon wolves and Wargs are in their train!”

It can certainly be argued that, both Goblins and Wargs far outnumbered the other three armies. The various descriptions give us clues to their approximate numbers. We are no longer talking about the few hundreds of Lake-Town men or the five hundred Dwarves under Dáin. Here, these two evil armies are almost certainly numbered in thousands.
“…in all the mountains there was a forging and an arming. Then they marched and gathered by hill and valley … a vast host was assembled.”
The word “host” is used again, but with a slightly different meaning to that associated with the Elven army. We are given an extra detail, another word “vast” to describe the army’s size. Again, it is clear that thousands gathered on the day of the battle and as it is about to commence, we read:
“… the Mountain’s feet black with a hurrying multitude.”

Tolkien wanted to reach the climax of ‘The Hobbit’ by using the idea of an epic battle fought against two extreme sides. “It was a terrible battle” we are told, as the fighting ensues. Further on, Tolkien delves into the strategic and tactical movements of the armies and amongst the words, we come to the second reference to army numbers (albeit a small one).
“As soon as the host of their (the Elves) enemies was dense in the valley, they sent against it a shower of arrows … a thousand of their spearmen leapt down and charged.”

So it is certain that five hundred Dwarves and one thousand Elves took part in the Battle of Five Armies and to understand the full import of the quote, one has to pay it careful attention. “A thousand of their spearmen”, paraphrased differently would literally mean: “a portion of the army’s spearmen”. In my opinion, that implies that the Elven army, at the very least, was divided into two: archers and spearmen. The archers were positioned to weaken the attack of the goblins whilst the spearmen would defend or attack. This phrase also suggests that out of a couple of thousand elves, one thousand were the first to engage in the fighting.

Although not part of the ‘five’ armies, the eagles also played an important role in the battle and it seems, at first, that even these creatures came with quite a large force:
“The eagles were coming down the wind, line after line, in such a host as must have gathered from all the eyries of the North.”
“Line after line”, “host”, “all the eyries” all describe the coming of a strong force but, as we shall see, we may have the wrong impression that there were many eagles.

Ch 18: The Return Journey
This is the last chapter in ‘The Hobbit’ to make reference to the battle. There is the appearance of Beorn and further references to the force of eagles.
“ … they [Eagles] gathered in great numbers …”
“But even with the Eagles they were still outnumbered.”

We have already confirmed that a vastly superior force of goblins took part in the battle and, as the surviving armies go back to their homelands we are told;
“Songs have said that three parts of the goblin warriors of the North perished on the day.”
“The elf-host was on the march … sadly lessened.”

Although losing much of its strength the elven army is still being referred to as a “host” so it makes sense to think that before the battle it had been quite a large force (thousands) and having lost many after the battle, it still remained fairly big.

Other Sources:
Moving now to Rateliffe’s ‘The History of the Hobbit’ (Volume 1) he makes an important point in Chapter VI: ‘Wargs and Eagles’:
“Given Tolkien’s continued interest in the eagles, it is odd that in the Battle of the Five Armies the wargs and goblins each count as a ‘people’ for purposes of the tally yet the eagles do not. Perhaps there are simply too few eagles present to be described as an ‘army’ (as seems to be the case with Beorn) …”
So the aforementioned “host” and “line after line” of eagles that take part in the battle, seem not to be considered as one of the armies, which would imply that the force was less than Tolkien implies; and might this apply to the other ‘established’ armies.

There is a short paragraph in Karen Wynne Fonstadt’s ‘Atlas of Middle-Earth’ estimating the armies’ numbers to a some degree:
“Dáin had brought ‘five hundred grim dwarves’; the Elvenking commanded at least a thousand spearmen, plus archers; and while Bard’s forces were uncertain, they may have been as few as two hundred, judging from the size of the town. In contrast, the enemy had ‘a vast host.’ ”

To understand the size of goblin forces, however, we need to consider the historical background and the orc colonies of the Misty Mountains, assuming the ‘goblins’ of ‘The Hobbit’ are the ‘orcs’ of Tolkien’s other stories. The final battle of the War of the Dwarves and the Orcs’ was the Battle of Azanulbizar in the year 2799 of the Third Age: We read in ‘The Lord of the Rings: The Return of the King’ – Appendix A; ‘Durin’s Folk’:
“When all was ready they [the Dwarves] assailed and sacked one by one all the strongholds of the Orcs that they could from Gundabad to the Gladden.”
“At last all the Orcs that fled before them were gathered in Moria, and the Dwarf-host in pursuit came to Azanulbizar”
“… the Orcs … outnumbered their enemies …”
“… he [Azog] saw that all his host … was in a rout, and the Dwarves went this way and that slaying as they would, and those that could escape from them were flying south”

The Tale of Years’ in Appendix B states ‘2800-64 – ‘Orcs from the North trouble Rohan. King Walda slain by them’ This was only a few years after the destruction of the Orcs at Azanulbizar and may only refer to those that escaped the battle alive and not necessarily that they had built up new strength.

“So it was that after Azanulbizar the Dwarves dispersed again. But first with great labour they stripped all their dead, so that Orcs should not come and win there a store of weapons and mail.”
This might suggest that there were still a few orcs around, but probably too few to pose any serious threat to Khazad-dûm. Even though they soon began to re-take control of the Dwarven mines when Balin was lost. So what do ‘The War of the Dwarves and the Orcs’ and Balin’s return to Moria have to do with the Battle of Five Armies? Why connect two events, one of which happened years before the Battle and the other years after it. Assuming that the orcs at the Battle of Five Armies came from the colonies in the Misty Mountains (as told in ‘The Hobbit’) from Moria and the North, including Mount Gundabad and if we can understand from past histories and what happened after the Battle, we might be able to perceive whether Orcs could multiply in huge numbers over a short period of time.

Now I refer to ‘Unfinished Tales’ – ‘The Quest of Erebor’ Though it is important to note that here we are not given any army numbers (which is the whole purpose of this discussion), but at the very least, we can make out how large the goblin army was at the Battle. From what has been said above, we can deduce that the Orcs were almost completely destroyed at the Battle of Azanulbizar, leaving the Misty Mountains free from their evil. But just over 142* years later, the orcs renewed their forces and launched the attack on the Lonely Mountain. Here, as is described in ‘The Hobbit’, three-parts of the orcs of the North, were destroyed that day. Once again, the North became free of their evil for many years.

Within 48 years of Battle of Five Armies, Balin returned to Moria and was lost (2989 TA). By that time the orc numbers had grown and, as we are told in ‘The Fellowship of the Ring’, the Fellowship was attacked by them.
[*The Battle of Azanulbizar took place in 2799 whilst the Battle of Five Armies occurred in the year 2941 of the Third Age, (Appenidx B; ‘The Tale of Years’, exactly 142 years later)].

So, after long deliberation I strongly believe that the goblin army (excluding wargs), was close to 30,000. One might not agree with such a high number, as compared to my figures for the elves, men and dwarves. How could such a large army lose against a small force?

However, considering the geography of the Lonely Mountain and the movements of the armies (as described in ‘The Hobbit’ and shown in ‘The Atlas of Middle Earth’), the small force of around 3,000 elves, men and dwarves, aided by the Eagles and Beorn could manage to hold off and, prevail against the massive host of 30,000 orcs. So this analysis concludes that the following figures represent approximate army strengths at the Battle of Five Armies and the numbers subsequent survivors.

Before the Battle
Elves – 2,000
Men – 300
Dwarves – 550
Eagles – 50
Goblins – 30,000
Wargs – 2,000

After the Battle:
Elves – 900
Men – 100
Dwarves – 350
Eagles – 40
Goblins – 0
Wargs – 0