Rest

Rest is the game mechanic that controls Characters' needs for sleep. A character with a higher rest value has slept recently, and is less tired than another character with a low rest level.

Levels of Rest

Characters' rest level is grouped into four thresholds: Rested, Tired, Very Tired, and Exhausted. Each threshold exhibits different effects on a character, especially their Thoughts. When a character's rest level is zero they may collapse from exhaustion; they will immediately begin sleeping on the ground wherever they are.

The rest levels are as follows:

Label	Rest
Rested	>= 28%
Tired	>=14% and <28%
Very Tired	>=1% and <14%
Exhausted	<=1%

Rest caps at 0% and 100%.

Rest Changes

Negative

When awake, rest goes down every 150 ticks (1/400 of a game day) depending on the character's current rest.

Rest threshold	Rest change per 150 ticks	Rest change per game day	Time between previous and next thresholds	Time since 100% rest
Rested (100 => 28)	-0.2375%	-95%	~0.758 days / ~18.189 hours	~0.758 days / ~18.189 hours
Tired (28 => 14)	-0.16625%	-66.5%	~0.211 days / ~5.053 hours	~0.968 days / ~23.242 hours
Very Tired (14 => 1)	-0.07125%	-28.5%	~0.456 days / ~10.947 hours	~1.425 days / ~34.189 hours
Exhausted (1 => 0)	-0.1425%	-57%	~0.018 days / ~0.421 hours	~1.442 days / ~34.611 hours

Positive

When a character rests in a bed, their Rest value increases over time. At 100% Rest Effectiveness and 100% Rest Rate Multiplier, a character requires 10.5 hours (26,250 ticks) to full rest from 0% to 100%.

 Every 150 ticks (2.5 seconds at 1x speed), rest increases by 100% * (Ticks in interval (150) / Ticks Per Game Day (60000)) * (Hours per day (24) / Sleep Hours for Full (10.5)) * Rest Effectiveness * Rest Rate Multiplier
 = 100% * (150 * 24) / (60000 * 10.5) * Rest Effectiveness * Rest Rate Multiplier
 = (100%/175) * Rest Effectiveness * Rest Rate Multiplier
 = ~0.57143% * Rest Effectiveness * Rest Rate Multiplier

175 of these 150-tick intervals is the 26,250 ticks (10.5 in-game hours) required to fully rest from 0%.

Multipliers

Rest Rate Multiplier is a character (pawn) stat that defaults at 1.0 and is based off blood pumping, metabolism, and breathing capacities (and thus is affected by relevant injuries, bionics, etc.)

Blood Pumping has a .3 weight
Metabolism has a .3 weight
Breathing has a .3 weight

Rest Effectiveness depends on the object the character is sleeping on:

Object	Rest Effectiveness at Normal quality	Rest increase per 150 ticks	Rest increase per full 24-hour game day
Sleeping Spot or Ground	0.8	~0.45714%	~182.857%
Bedroll	0.95	~0.54286%	~217.143%
Bed	1.0	~0.57143%	~228.571%
Royal Bed	1.05	0.6%	240%

and the quality of that object:

Quality	Rest Effectiveness Multiplier
Awful	0.86
Poor	0.92
Normal	1.0
Good	1.08
Excellent	1.14
Masterwork	1.25
Legendary	1.6

Therefore, when a character with 100% Rest Rate Multiplier reaches the Tired threshold (28%), it takes them this long to return to full (100%) rest:

Object	Ticks to Full Rest	Hours to Full Rest	% of Day to Full Rest
Sleeping Spot / Ground (0.8)	23,625	‭9.45	39.375%
Normal Bed (1.0)	18,900	7.56	31.5%
Legendary Royal Bed (1.05 * 1.6 = 1.68)	11,250	4.5	18.75%

Analysis

There exists a balance point for every type/quality of bed (and character, if that character has offsets to Rest Rate Multiplier or Rest Fall Rate), in which the hours spent sleeping and the hours spent awake during a 24-hour period precisely balance. This is ultimately a piecewise equation, as the rest fall rate is piecewise based on the current rest level (see above). We can ignore the Exhausted category, as a character must spend >24 hours awake (if starting at 100% rest) before reaching that threshold.

As long as the character is awake for less than 18.189 hours per day, however, this is a single-part equation, as the character will never reach Tired. The percentage of the day that the character may stay awake, expressed as a decimal value, with a given RestMult (equal to Rest Effectiveness * Rest Rate Multiplier) is reached by solving the following equation for %DayAwake:

 0.95 * %DayAwake = (1 - %DayAwake) * (24/10.5) * RestMult

This gives the following equation:

 %DayAwake = (320 * RestMult) / (320 * RestMult + 133)

At 1.0 RestMult (normal unmodified character in a normal quality regular bed), this gives a value of 70.64% of the day awake, or ~16.95 hours. Higher RestMults will grant more hours per day awake per this equation, up to 18.189 hours (75.789% of the day) awake.

Beyond that point, we need a piecewise equation. The RestMult needed to be awake for 18.189 hours per day (0.75789 %DayAwake) is 1.301, which can be achieved with only a masterwork Royal Bed. After this point, we can use a fixed value for the ~75% of the day awake before hitting Tired, which results in a 72% drop in rest, and then compute the remainder of the time awake off of the rest fall rate when Tired (66.5% per day rather than 95% per day). This can be found by solving:

 0.72 + (%DayAwake - (0.72/0.95))*0.665 = (1 - %DayAwake) * (24/10.5) * RestMult

This gives:

 %DayAwake = (16000*RestMult - 1512) / (16000*RestMult + 4655)

At 1.3125 RestMult (an unmodified character in a masterwork Royal Bed), which is just past the threshold where this equation is needed, this gives a value of 75.962% 0f the day awake, or 18.231 hours.

At 1.68 Rest Effectiveness (the legendary quality Royal Bed in the table above) and a character with the Quick Sleeper trait (50% Rest Rate Multiplier), a Bionic Heart (+25% Blood Pumping = 7.5% Rest Rate Multiplier), and a Bionic or Royalty stomach (all of which are +25% part efficiency -> +12.5% Metabolism -> 3.75% Rest Rate Multiplier), for a net of 1.5*1.075*1.0375 = 1.673 Rest Rate Multiplier, the RestMult = 1.68 * 1.673 = 2.811. At that level, the character can be awake for 87.573% of the day, or 21.017 hours.

In theory, there also exists a point at which the Very Tired piece of the equation becomes a factor, but this would require a pawn to be awake for at least 96.84% of the day (23.242 hours). This would require a RestMult of at least 11.915 (ie. 1191.5%), which is impossible to hit in the base game (and even with most mod setups), and thus can be ignored.

If the character is using a Circadian assistant, their rest fall rate is reduced by 20%, meaning it takes 25% longer to reach each threshold. The equations in this case must be re-derived (derivation is left as an exercise for the reader), but the simple answer is:

A character otherwise unmodified except for the Circadian Assistant, using a normal quality bed, can be awake for ~75.047% of the day (~18.011 hours), about 6.3% more of the day than without the implant.
An otherwise-unmodified character in a masterwork Royal Bed can be awake for ~79.787% of a day (~19.149 hours), about 5% more of the day.
The above bionically-modified Quick Sleeper pawn in a legendary quality Royal Bed, with the addition of a Circadian Assistant, could be awake for ~89.421% of a day (~21.461 hours), about 2.1% more of the day.
None of these characters would ever reach "Tired", which takes ~94.737% of a day, or ~22.737 hours, with a Circadian Assistant installed.