Do the maths

(Good input from Fulli and Red_Shadow in the other answer):

Canon

(is it? official link please)

The Imperium of Man has tens of quadrillions of citizens scattered across millions of worlds in the Empire.

Numbers

• Definition of a quadrillion in UK and AmE would be 10¹⁵, or 1,000,000,000,000,000.
• Tens of quadrillions would simply be, let's be generous and have 90 of q. == 9 x 10¹⁶

Aside:

• Millions of worlds at, say 900 millions == 9 x 10⁸
• Makes 900 Million people per world on average, which is really not too much

Population maths

Using a reproduction rate of 1,1 (daughters per mother) and a generation duration of 35 years give or take, we get roughly 900 generations over a span a bit more than 30,000 years.

To get to the current population (based on the net reproduction rate only), we have to multiply the starting population x 1,1⁹⁰⁰.

• 1,1^900 =~ 1,8 x 10^37 (even with a base population of 1 (!))
• Let's some simplistic rounding and simply use 10^40 as the expected number
• If we were to use 20,000 years as reproduction timespan, we'd get something like 10^25

If we take "tens of quadrillions" to mean 10^17, then even with a reproduction rate of 1,1 per generation this means we're left with a factor of 10^8 (-> 25-17), that is 100 million times less humans than there could be.

In other words, to get at a population of 10^17 over (even only) 20,000 years, we have to use a net reproduction rate (with a generation span of 35 yrs) of 1.071: That means, per 100 women, you'll have 107 daughters, that is, only 7 out of hundred women would have more than one daughter.

So, if anything, the Imperium is thoroughly under-populated (as well as it should be given the setting.)

Do the maths

(Good input from Fulli and Red_Shadow in the other answer):

Canon

(is it? official link please)

The Imperium of Man has tens of quadrillions of citizens scattered across millions of worlds in the Empire.

Numbers

• Definition of a quadrillion in UK and AmE would be 10¹⁵, or 1,000,000,000,000,000.
• Tens of quadrillions would simply be, let's be generous and have 90 of q. == 9 x 10¹⁶

Aside:

• Millions of worlds at, say 900 millions == 9 x 10⁸
• Makes 900 Million people per world on average, which is really not too much

Population maths

Using a reproduction rate of 1,1 (daughters per mother) and a generation duration of 35 years give or take, we get roughly 900 generations over a span a bit more than 30,000 years.

To get to the current population (based on the net reproduction rate only), we have to multiply the starting population x 1,1⁹⁰⁰.

• 1,1^900 =~ 1,8 x 10^37 (even with a base population of 1 (!))
• Let's some simplistic rounding and simply use 10^40 as the expected number
• If we were to use 20,000 years as reproduction timespan, we'd get something like 10^25

If we take "tens of quadrillions" to mean 10^17, then even with a reproduction rate of 1,1 per generation this means we're left with a factor of 10^8 (-> 25-17), that is 100 million times less humans than there could be.

In other words, to get at a population of 10^17 over (even only) 20,000 years, we have to use a net reproduction rate (with a generation span of 35 yrs) of 1.071: That means, per 100 women, you'll have 107 daughters, that is, only 7 out of hundred women would have more than one daughter.

So, if anything, the Imperium is thoroughly under-populated (as well as it should be given the setting.)

Do the maths

(Good input from Fulli and Red_Shadow in the other answer):

Canon

(is it? official link please)

The Imperium of Man has tens of quadrillions of citizens scattered across millions of worlds in the Empire.

Numbers

• Definition of a quadrillion in UK and AmE would be 10¹⁵, or 1,000,000,000,000,000.
• Tens of quadrillions would simply be, let's be generous and have 90 of q. == 9 x 10¹⁶

Aside:

• Millions of worlds at, say 900 millions == 9 x 10⁸
• Makes 900 Million people per world on average, which is really not too much

Population maths

Using a reproduction rate of 1,1 (daughters per mother) and a generation duration of 35 years give or take, we get roughly 900 generations over a span a bit more than 30,000 years.

To get to the current population (based on the net reproduction rate only), we have to multiply the starting population x 1,1⁹⁰⁰.

• 1,1^900 =~ 1,8 x 10^37 (even with a base population of 1 (!))
• Let's some simplistic rounding and simply use 10^40 as the expected number
• If we were to use 20,000 years as reproduction timespan, we'd get something like 10^25

If we take "tens of quadrillions" to mean 10^17, then even with a reproduction rate of 1,1 per generation this means we're left with a factor of 10^8 (-> 25-17), that is 100 million times less humans than there could be.

IN other words, to get at a population of 10

Do the maths

(Good input from Fulli and Red_Shadow in the other answer):

Canon

(is it? official link please)

The Imperium of Man has tens of quadrillions of citizens scattered across millions of worlds in the Empire.

Numbers

• Definition of a quadrillion in UK and AmE would be 10¹⁵, or 1,000,000,000,000,000.
• Tens of quadrillions would simply be, let's be generous and have 90 of q. == 9 x 10¹⁶

Aside:

• Millions of worlds at, say 900 millions == 9 x 10⁸
• Makes 900 Million people per world on average, which is really not too much

Population maths

Using a reproduction rate of 1,1 (daughters per mother) and a generation duration of 35 years give or take, we get roughly 900 generations over a span a bit more than 30,000 years.

To get to the current population (based on the net reproduction rate only), we have to multiply the starting population x 1,1⁹⁰⁰.

• 1,1^900 =~ 1,8 x 10^37 (even with a base population of 1 (!))
• Let's some simplistic rounding and simply use 10^40 as the expected number
• If we were to use 20,000 years as reproduction timespan, we'd get something like 10^25

If we take "tens of quadrillions" to mean 10^17, then even with a reproduction rate of 1,1 per generation this means we're left with a factor of 10^8 (-> 25-17), that is 100 million times less humans than there could be.

In other words, to get at a population of 10^17 over (even only) 20,000 years, we have to use a net reproduction rate (with a generation span of 35 yrs) of 1.071: That means, per 100 women, you'll have 107 daughters, that is, only 7 out of hundred women would have more than one daughter.

So, if anything, the Imperium is thoroughly under-populated (as well as it should be given the setting.)