Our DM gave us what seemed to me to be a very hard encounter so I checked out the DMG to see whats up. Note this was the only encounter of the day and we generally have 1-4 encounters per day.

We are a group of four level 7 players, and we met three frost giants.
The thing is, we crushed them even though they downed some of our party members, and when I looked at the DMG it seemed like the encounter was in the average-hard range for our group if we were level 20, or hard-deadly for our team if we were level 15. He even gave the frost giants some ridiculous version of net with a DC 17 Strength check to get out instead of the normal DC 10.

XP THRESHOLDS BY CHARACTER LEVEL

7th, easy 350, medium 750, hard 1100, deadly 1700

14th deadly 5700

15th hard 4300, deadly 6400

20th medium 5700

Frost giant: Challenge 8 (3,900 XP) Hit Points 138

Please tell me if I am doing something wrong here:

Say we want a deadly encounter for our four level 7 characters.

1. Determine XP Thresholds
   Deadly for level 7 is 1700




2. Determine the Party's XP Threshold
   4*1700=6800




3. Total the Monsters' XP
   3*3900=11700




4. Modify Total XP for Multiple Monsters
   The multiplier for 3 - 6 monsters is *2. 11700*2=23400 (23400/4 would be 5850, more than what is budgeted in a deadly encounter for characters with twice our level)

Please help me out here, did I do the calculation correctly and if I did are we somehow ridiculously OP?

Our paladin and cleric had Gauntlets of Ogre Power; our rogue had Bracers of Archery; our fighter had Quiver of Ehlonna

If anyone is curious, the fight went something like this:

1. Paladin used Vow of Enmity, hit for a ton of damage. His found steed also critted.
   
   Rogue managed to crit with sneak attack


2. Cleric used Spirit Guardians


3. Frost giant used net with DC 17 on paladin


4. Frost giant dropped the paladin to zero HP in one turn (advantage because of restrained, one crit one hit)


5. Frost giant used net on cleric and missed.


6. Fighter (ranged) missed and ran away on horse


7. Paladin failed death save


8. Paladins steed broke out of the net (since paladin was mounted DM trapped both in the net)


9. Rogue did normal damage


10. Cleric healed the paladin with healing word and used dodge action


11. Frost giant killed steed


12. Frost giant missed cleric


13. Frost giant hit cleric, he survived


14. Fighter killed the first of the three giants.
    
    (something will probably be inaccurate)

You were just over "1 day's XP budget / "five minute adventure day"

In the Basic Rules p. 166/DMG p. 84, there's another table that lays out the estimated "adjusted XP" for an entire adventure day. For your party: 7th /5,000/ x 4 = 20,000. (Your adjusted XP calculation was correct at 23,400).

The usual adventure day is designed with "6-8 encounters of medium-hard" difficulty. You had one big encounter. From what I've seen as a DM, three hard to deadly, or one "more than deadly" is often handled by the PC's if they are tactically astute and work as a team.

• 
  

  Note: the XP encounter tables do not make any assumptions about
  having magic items, so your party did about as I'd expect: you could
  spend resources without worrying about another encounter, and your
  magical items were at least a small help. The dice were perhaps
  your friend with that early crit from the rogue.

  
  
  

  It was still a dangerous fight, as you described it. As I found out in the Giants module from Tales of the Yawning Portal, when a giant crits the HP come in bunches.

  
  

A deadly encounter is described as follows:

Deadly. A deadly encounter could be lethal for one or more player
characters. Survival often requires good tactics and quick thinking,
and the party risks defeat. (Basic Rules, p. 165 (same as DMG))

Other factors: luck and allies.

Yes, your encounter was deadly; there was a decent chance the Paladin dies from that crit. A couple of factors seem to have contributed: luck and the NPC ally.

1. There is some element of luck involved in the rogue's early crit.
   And the steed's crit.


2. An NPC who becomes a target can make a big change in the difficulty
   since the party is subjected to fewer attacks. The impact of the NPC on this fight is hard to assess, though your follow up comment indicates that the NPC didn't do a great deal before the battle ended.

The Adventuring Day

Assuming typical adventuring conditions and average luck, most
adventuring parties can handle about six to eight medium or hard
encounters in a day. If the adventure has more easy encounters, the
adventurers can get through more. If it has more deadly encounters,
they can handle fewer (Basic Rules, p. 166)

Encounter design is an inexact science

We have a variety of questions and answers here that point to how swingy combat is, and how a given encounter's difficulty is an estimate rather than a hard and fast rule.

1. Good tactics can make an encounter a lot easier. Bad tactics can turn into a party wipe/TPK. Also, if a Paladin's smites are a successful nova strike, that can shorten encounters by reducing the number of attacks on the party as opponents are felled.




2. Some magical items have a significant swingy effect on some encounters. For example, in my brother's campaign the party's level 5 gnome rogue has a broom of flying. In outdoor encounters, he's a heck of a force multiplier. Indoors, not as much.

I'm not certain that describing the fight as "Deadly" for your level is wholly inappropriate; however, there is some Math we need to knock out first.

Frost Giants are weaker than their Challenge Rating would suggest

In the Dungeon Master's Guide, the advice for creating custom monsters provides advice on how to stat creatures based on what their Challenge Rating should be, including a table for basic stats:

If all you need are simple stats for a monster of a particular challenge rating, follow the steps here. If you want to create something more akin to the monster stat blocks in the Monster Manual, skip ahead to the "Creating a Monster Stat Block" section.

begin{array}{|l|l|l|l|l|l|l|}
hline
text{CR} & text{Prof.Bonus} & text{Armor Class} & text{Hit Points} & text{Attack Bonus} & text{Damage/Round} & text{Save DC} \ hline
text{0} & text{+2} & text{≤ 13} & text{1-6} & text{≤ +3} & text{0-1} & text{≤ 13} \ hline
text{........} & text{........} & text{........} & text{........} & text{........} & text{........} & text{........} \ hline
text{8} & text{+3} & text{16} & text{176-190} & text{+7} & text{51-56} & text{16} \ hline
text{........} & text{........} & text{........} & text{........} & text{........} & text{........} & text{........} \ hline
end{array}

—Creating Quick Monster Stats, Dungeon Master's Guide, pg. 274

A few things stand out immediately, comparing to the Frost Giant's Stats:

• The Frost Giant's health is too low (138 vs the expected 176-190)


• The Frost Giant's AC is too low (15 vs the expected 16)


• The Frost Giant's Damage is too low (25x2 vs the expected 51-56)


• The Frost Giant's Attack Bonus is too high (+9 vs the expected +7)

The only major feature is the Net†, but it's an optional feature of the Frost Giants introduced in a specific campaign module, meaning it's not been considered in the original CR calculations. Other than that, the Frost Giant does not have any special features or abilities, aside from a (trivially unimportant) immunity to Cold Damage, meaning that in addition to lower than expected stats, it also doesn't have features that aid it.

^{† Brief Editorial on the Net: you described it as "some ridiculous version of net with a DC 17 Strength check to get out instead of the normal DC 10.". I'm not really interested in adjudicating the capabilities of this feature and how powerful it is, but it's worth noting that this is the stats provided in Storm King's Thunder (pg. 246) for this ability, so while it is more powerful than a normal net, it's what the campaign designers intended. I don't know whether your party is using that campaign module or not.}

The damage and attack discrepancies mostly equal out to the expected offensive capabilities of a CR 8 creature (damage is equivalent to a CR7, Attack bonus 2-greater-than-normal means add 1 for an Offensive CR of 8) but the health and AC instead are representative of a CR5 creature. On average, that puts a Frost Giant around more of a CR of 6.5 than 8, meaning that budgeting encounters using their normal CR is going to result in easier-than-normal fights.

In fact, using the normal budgeting technique:

• 2,300XP for a CR6 creature
  
  
  
  
  • I'm rounding down because in my experience, low HP tends to count more than low DPR in terms of affecting encounter difficulty
  
  
  
  


• x3 for 3 creatures, 2,300x3 == 6,900XP


• x2 for Group Size of 3-6 creatures, 6,900x2 == 13,800XP


• Deadly Encounter threshold for a party of 4 is 1,700XP per party member, or 6,800XP

With all these adjustments, it still seems like the encounter should be relatively deadly—but I would argue that that's a pretty reasonable assessment given your account of how the fight went.

Deadly is an appropriate description of how the fight went

Bear in mind that your Paladin went down in a single turn! You were able to recover him with some judicious use of healing, but it's not hard to see how this fight could have gone very south very quickly depending on the context. If the third Frost Giant had chosen to attack the Paladin after they went down, before the healing, they would have all-but-certainly died, and this "Deadly" encounter would have lived up to its name.

Deadly does not imply unwinnable, it just means that the fight will require some very apt strategic aptitude on the part of the players, or some degree of sheer luck, to prevent any member of the party from dying. Your party managed to survive the fight, in part because your party appears to be quite well balanced, with characters that have either exceptional survivability (Paladin, Rogue, Fighter) or plentiful healing capabilities (Cleric, Paladin) or high Damage output (Paladin, Rogue) or potent support capabilities (Cleric, Paladin). In total, unless your party has abysmal ability scores, I would expect this party composition to punch above their pay-grade, so to speak.

One last thing I should mention: the thresholds for per-encounter design are important guidelines, but also important is the XP-per-day thresholds, which imply strongly the maximum amount of combat a party can take over the course of a day—which they very well could blow in a single combat encounter given an especially powerful foe. Indeed, for a 7th level character, the XP-per-day threshold is 5,000XP, and multiplied by four characters, puts the total at 20,000XP, which now exceeds the budget provided by the three Frost Giants under my calculations (13,800XP), and is only slightly eclipsed using the original total (23,400XP).

Conclusion

So in total there's a few important takeaways:

• Frost Giants aren't as strong as their CR ought to imply,


• The encounter rated as Deadly, but as less powerful than what it should take to exhaust a party of all their resources for the day,


• But it's still fair to call the encounter Deadly, especially given how much damage got poured into your paladin in a single turn, and how differently the fight could have gone with less luck on the part of your party,


• But also your party is well-optimized to handle an unusually dangerous encounter.

So take a small amount of pride in knowing that you fought back against a threat that was above average for your level, but also remember that things could have gone much worse.

Encounter Design

Xirema and KorvinStarmast have done an excellent job in analyzing your particular encounter, but I want to get a bit more into encounter design and the tools for calculating difficulty.

In my experience as DM and player, I've found that the encounter calculators are really not all that useful in terms of what's reasonable during a day. They give a decent guideline, but in the groups I've played with, unless the encounter is hard/deadly, then it's been way too simple and didn't actually require resources to get through successfully.

I've asked about why have easy encounters here and there have been some excellent reasons. But in terms of resource expenditure, I've found that in order to make an encounter challenging, it needs to be hard/deadly. And that's whether or not I'm running the 5 minute adventure day (which we tend not to do), but I'd say my tables run 1-3 combat encounters daily which is similar to what you're experiencing. In order to make those 'challenging', we end up having encounters that rank hard/deadly. And we do those for nearly all of the encounters. Some are definitely easier, but rarely (if ever) do we get a cakewalk.

Monster Tactics

This is the greyest area in DMing an encounter. Understanding how you plan on playing your monsters and how much they act intelligently/together and whether or no their tactics are logical is one of the hardest things a DM manages (besides people!)

You can have an encounter that on paper is beyond deadly. But if the DM doesn't play it that way, then it won't be.

Alternatively, luck can also play a huge factor. Whether it's good luck or bad depends on the side, but the roll of the dice guys a looooong way in determining how an encounter goes.

Your Frost Giants

Your DM opted to play the Frost Giants you found in a way that helped set you up for victory. Had your DM begun with ranged Rock attacks before you were even in range, your party would already have been softened up. The DM then followed up by opting for the Net attack rather than the multiattack with the Great Axe. Bypassing the damage option for battlefield control further leans in your favor.

Additionally, your party got some lucky swings and used some big resources to win this fight. Crits, especially if paired with Sneak Attack or Smites go a very long way. But you also saw what successful hits from the Giants will get you. Even without the advantage, they had a +9 to hit. Odds were, they were gonna hit your party. Even if they didn't crit, that's a lot of damage when paired with the multiattack.