How many unique states can a human brain be in?

People like to say the brain has more connections than there are stars in the universe. It doesn't. The real count is stranger than the slogan, and working it out teaches a good deal about how a brain holds information.

This article counts the states a human brain could, in principle, be in. That means every configuration with any chance at all of occurring, and the ones you will actually experience turn out to be a vanishing sliver of them. We will fix what a “state” is, add up the options one layer at a time, and then look closer: down to the molecules, and up to the ceilings that physics places on any object of the brain's size, weight and temperature.

You need nothing beyond school maths. Each idea is introduced before it is used, and each number comes with its source or its arithmetic. Here is where we end up.

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Against all of these, one fact holds steady: a lifetime is short. If every new state costs the brain at least one erased bit, eighty years at 20 watts pay for about 1.7 × 10³¹ of them, a number with 32 digits. Even the quantum speed limit, which no object can beat, allows no more than about 10⁶⁰. Either is nothing beside numbers with quadrillions of digits.

Here is the estimate most people sketch first. It deserves to be taken seriously, because its instincts are good and its mistakes are instructive.

Four repairs turn this into something we can calculate.

Factorials count queues, and wiring is something else

A factorial answers one question: in how many orders can I line these things up? Three people can queue in 3 × 2 × 1 = 6 ways. A wiring diagram asks two different questions.

• How many connections are possible? Each of N neurons could send to each of the others, giving N × (N − 1), which for large N is as good as N². For 86 billion neurons that is 7.4 × 10²¹.
• How many wiring diagrams are possible? Each possible connection is either present or absent, so the count doubles with every one of them: 2 multiplied by itself N² times.

With small numbers the difference is easy to see.

For the real brain, 86 billion factorial is about 10^9 × 1011, a number with 900 billion digits. That is enormous and still far too small. The count we reach below has twenty thousand times as many digits.

The stars

The European Space Agency's rough census²¹ puts the number of stars in the observable universe between 10²² and 10²⁴. The brain's 7.4 × 10²¹ possible connections fall just short of the low end. Its actual connections, somewhere between 10¹⁴ and 10¹⁵, outnumber the stars in our own galaxy about a thousand to one, and the universe's not at all. What beats every count of things in the cosmos, including the roughly 10⁸⁰ atoms in the observable universe, is the number of ways the wiring could have been arranged.

A synapse doesn't choose from the whole pharmacy

There are well over a hundred known transmitter molecules, and one review puts the figure at two hundred or more.⁹ But a neuron releases a small set, fixed by the type of cell it is: typically one fast transmitter such as glutamate or GABA, often with one or more slower-acting peptides alongside. The message also depends on the receiver. The same molecule can excite one cell and quiet another, according to which receptors are waiting for it.

Because we are after an upper bound, we will still let every synapse choose freely among 140 options. That is too generous, and as you will see it barely matters.

The radio analogy, corrected

QAM, the scheme behind Wi-Fi and mobile data, packs bits into both the amplitude and the phase of a carrier wave. Neurons do something related. The signal that travels along a nerve fibre is a spike, and spikes are all-or-nothing: nearly the same height every time. On the wire, information lives mostly in when spikes happen. Not only there: the slower voltage between spikes can spread along the fibre and change how much the far end releases, and some neurons, such as many of the retina's bipolar cells, use graded voltages and no spikes at all.³⁹ A single motion-sensing neuron in a fly's visual system has been measured carrying up to 90 bits per second this way, with timing that matters down to about a millisecond.¹⁰ Phase is real too. In the hippocampus, a cell fires at steadily earlier points of a background rhythm as an animal crosses the spot that cell responds to, so the phase of each spike reports how far across it is.¹¹

Amplitude enters at the synapse, the junction between two neurons. When a spike arrives, the synapse releases a variable number of transmitter packets onto a variable number of receptors. That graded strength is what learning adjusts. So the brain keeps timing on the wire and amplitude at the junction.

The fourth instinct, the hierarchy, needs no repair. It needs names, which arrive in layer four.

Physicists describe a system with a state space, also called a phase space: an imaginary space with one axis for every quantity needed to describe the system completely. A single point in it is one complete state, everything about the system at one instant. As the system changes, the point moves and traces a path. (In quantum mechanics the point blurs into a smudge, and a Schrödinger's cat is two smudges at once: Nº 10.)

Two consequences follow, and both matter for the count.

A state is not a signal. A pattern of spikes unfolding over a second is a path, and a path adds no room to the space it runs through. Timing counts toward the size of the space only through the quantities that hold it at a single instant: voltages, whether each ion channel is open or shut, calcium levels, how long a given fibre takes to carry a spike.

Smooth quantities need a grain. A voltage can take infinitely many values, so the count is infinite unless we say how different two values must be to count as different. Noise settles that. Two voltages closer together than the random jitter cannot be told apart by anything downstream. Every figure on this page is a count of distinguishable states, and that is why it is finite.

The rule for inclusion is that a state counts if the brain has any chance of reaching it, however small. This rule is more radical than it sounds. Heat keeps every molecule jiggling, so every arrangement of the brain's atoms has some chance, including arrangements that are no longer a brain. The answer therefore depends on how closely you look, which is why the table above has four rows.

Counting in bits

If a system has W possible states, naming one of them takes log₂ W bits, the number of yes-or-no questions needed to pin it down. A coin has 2 states and takes 1 bit. A byte has 256 states and takes 8.

Bits earn their place here for one reason. When parts are independent, their states multiply and their bits add. Two bytes have 256 × 256 = 65,536 states and 8 + 8 = 16 bits. So we will add up bits per synapse, multiply by the number of synapses, and convert back to a count of states only at the end.

That conversion produces a tower such as 10^{1.8 × 1016}. Read it one level at a time: the exponent, 1.8 × 10¹⁶, is roughly how many digits the number has, and the upper exponent, 16, tells you roughly how many digits that count has. 10¹⁶ is a number with 17 digits. 10¹⁰¹⁶ is a number with ten quadrillion digits.

Neurons. The standard figure is 86 billion. It comes from a 2009 study that dissolved the brains of four men into a suspension of cell nuclei and counted them, arriving at 86.1 billion give or take 8.1 billion.¹ A 2025 re-analysis argues that four brains cannot pin the average down that tightly: the 95% confidence interval for the average is about 73 to 99 billion, and the same method applied to five elderly women gave 61 to 73 billion.² The original group has defended the 86 billion figure.²³ About four-fifths of the neurons sit in the cerebellum at the back of the head, with the cortex holding most of the rest. A similar number of non-neuronal cells, mostly glia, fills in around them.

Synapses. Counting under the electron microscope and scaling up gives about 1.5 × 10¹⁴ synapses in the neocortex, around 7,000 for each of its neurons.^24,3,4 Extending that to the whole brain gives about 2 to 3 × 10¹⁴;⁵ the round 10¹⁵ of textbooks has no firm primary count behind it. We want an upper bound, so we take 10¹⁵.

The maps. These figures are no longer pure extrapolation. In 2024 a team from Harvard and Google imaged one cubic millimetre of human cortex and reconstructed it automatically: about 57,000 cells, some 16,000 of them neurons, and 150 million synapses, from 1.4 petabytes of electron-microscope images.⁶ In 2025 the MICrONS project did the same for a cubic millimetre of mouse visual cortex, finding more than 200,000 cells and 523 million synapses.⁷ Beforehand it recorded the activity of some 75,000 of those neurons. In 1979 Francis Crick had named that pairing, the wiring of a cubic millimetre and the firing of its neurons, as an example of asking for the impossible.²⁵ In 2024 an entire adult fruit-fly brain was mapped at the same level: about 140,000 neurons and 50 million synapses.⁸ In 2026 two teams mapped a fly's whole central nervous system, brain and nerve cord together, one in a female and one in a male; the male's holds about 167,000 neurons.^33,29 A human brain is about 1.2 million cubic millimetres. Imaged the same way it would fill more than a zettabyte, which is a trillion gigabytes.

Is 10¹⁵ really a ceiling? Synapses take up room. Classical counts put cortex at up to about a billion synapses per cubic millimetre,⁴ and the 2024 human sample found 150 million in its cubic millimetre. Even at the denser figure, 1.2 million cubic millimetres of brain hold about 10¹⁵. A brain in which every neuron connected to every other would need 7 × 10²¹ synapses and, at that packing, about 7,400 cubic metres, the volume of three Olympic swimming pools. Such a brain has zero probability of existing inside a skull, so its wiring diagrams don't count.

Now the count itself. Each layer asks what one synapse could be, in bits, at the resolution set by noise.

Layer 1: the wiring, 24 bits per synapse

We have S = 10¹⁵ synapses to place among N² = 7.4 × 10²¹ possible sender-and-receiver pairs. The number of ways to choose is a binomial coefficient, and when the choice is sparse its logarithm has a simple form:

log₂ (ways to wire) ≈ S × log₂(e · N² / S)

With our numbers the bracket comes to 2 × 10⁷, so each synapse costs 24.3 bits. Think of it as an address. Naming one neuron out of 86 billion takes 36.3 bits, and a connection names two, for 72.65. Then comes a discount of 48.39 bits, because synapses are interchangeable: swapping two of them leaves the same brain, so the count must be divided by every possible ordering of the S synapses. This is where factorials belong in the calculation. They sit in the denominator and shrink the answer.

This count also lets any neuron contact any other, anywhere in the brain. A real axon can only make a synapse where it passes close to a dendrite. If each neuron could reach only 10⁵ to 10⁶ partners (an illustrative range, this page's estimate), this layer would shrink to about 5 to 8 bits, and the total to about 41 to 45 bits per synapse; the upper exponent of the final answer would still be 16. The calculator lets you try it. We keep the larger figure anyway, as a deliberate overcount: a typical diagram in this count scatters each neuron's partners across the whole brain, which would take far more axon than a skull can hold, the same kind of objection that rules out all-to-all wiring in the parts list. An upper bound is allowed to be loose.

Wiring total: 2.4 × 10¹⁶ bits.

Layer 2: the chemistry, 7 bits per synapse

One choice among 140 transmitters is log₂ 140 = 7.1 bits. If we were strict and fixed the transmitter by neuron instead of by synapse, this layer would shrink to 86 billion × 7 bits, about 6 × 10¹¹, and vanish from the total.

Layer 3: the strength, 4.7 bits per synapse

This is the one layer that has been measured. In 2015 a group at the Salk Institute and the University of Texas reconstructed a sliver of rat hippocampus in three dimensions and found pairs of synapses that shared both the same sending fibre and the same receiving branch. Such pairs should share the same history of activity, so the authors treat any difference in their size as noise. Size stands in for strength here, and recordings from single synapses in the cortex show that a bigger contact tends to pass a bigger signal.⁴⁰ The pairs turned out nearly identical, close enough to distinguish 26 sizes across the full range, or 4.7 bits.¹² Reaching that precision, the authors estimate, requires the synapse to average its activity over many release events: minutes, at low firing rates.

A 2024 follow-up that applied Shannon's information theory directly found 4.1 to 4.6 bits in the same region.¹³ Related work found fewer distinguishable sizes in a neighbouring region, the dentate gyrus: about 2.7 bits, rising to about 3.7 after the synapses were strengthened experimentally.²² In mouse visual cortex, a 2022 reconstruction found that pairs of synapses joining the same two cells agree mainly on whether they are strong or weak; the finer variation in size of one says nothing about the other.³⁴ Capacity evidently varies across the brain. We take 4.7 everywhere, the highest of these values.

Layer 4: the slow variables, about 15 bits per synapse a guess

Here is the “derivatives of derivatives” instinct. A synapse's strength is not its only memory. How readily that strength changes is itself adjustable and depends on the synapse's past, a property called metaplasticity: the plasticity of plasticity.¹⁴

Theorists have shown why a brain would want this. A synapse with one adjustable number forgets quickly, because new learning overwrites old. Give it a chain of hidden variables, each slower than the last and each feeding the next, and its memories last far longer.^15,16 Alongside that chain sit the synapse's short-term habits (whether repeated use makes it briefly stronger or weaker), the mix of receptor subtypes it carries, and the slow chemical weather of modulators such as dopamine and serotonin.

Nobody has measured how many distinguishable states this layer holds. We assign 15 bits per synapse, the equivalent of five hidden variables at 3 bits each, and mark it as a guess. The calculator lets you change it.

Layer 5: the fast activity, about 10 bits per synapse a guess

Last come the quantities that change from one millisecond to the next: the local voltage, how many of its ion channels are open, the calcium concentration, how many transmitter packets are docked and ready. We assign 10 bits per synapse, also a guess.

The spikes themselves hardly register. At millisecond resolution each neuron either fired or didn't, one bit apiece, for 8.6 × 10¹⁰ bits in all. That is about a millionth of the total.

The total

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Sixty-one bits per synapse, times 10¹⁵ synapses, is 6 × 10¹⁶ bits. Converting back, 2 raised to that power is 10^{1.8 × 1016}: a 1 followed by 18 quadrillion zeros. Set in ordinary type, the number would run about 250 times the distance from the Earth to the Sun.

One pattern in the table is worth noticing. Every layer came out as a handful of bits per synapse. More neuroscience would add more handfuls, and the total would stay pinned near the number of synapses times a few tens of bits. Moving that total by many orders of magnitude takes a change of resolution, which is the subject of the ceilings.

The neural count ignores everything smaller than a synapse. Looking closer raises the number, and physics says exactly how far it can rise.

Every protein

A synapse is a machine built from molecules, each of which can be in different shapes, places and chemical conditions. A 2014 study counted the proteins in an average nerve terminal from rat brain, the sending half of a synapse, and built a model containing about 300,000 of them.¹⁷ Across 10¹⁵ synapses that is 3 × 10²⁰ proteins in the terminals alone. Allow each between one and ten bits of condition and the terminals alone hold 3 × 10²⁰ to 3 × 10²¹ bits. With the 2 to 3 × 10¹⁴ synapses actually estimated instead of our generous 10¹⁵, and counting the rest of each cell, 10²⁰ to 10²² bits at molecular resolution is a fair bracket. This figure is rough arithmetic, since no one has measured it.

Every arrangement the heat allows

Thermodynamics already keeps track of the count of microscopic arrangements available to a warm object, W: the object's entropy is k ln W, and it can be looked up. The brain is about 1.4 kilograms and mostly water. Water's entropy is about 70 joules per kelvin for each mole, and treating the whole 1.4 kilograms as water (78 moles) overstates it only a little:

78 mol × 70 J/(mol·K) ≈ 5,500 J/K  →  5,500 ÷ (k ln 2) ≈ 5.7 × 10²⁶ bits

Here k is Boltzmann's constant, and dividing by k ln 2 converts entropy into bits. This is the honest version of “every state with a non-zero chance”: strictly, heat gives some tiny chance to far more states, but entropy counts the ones that carry essentially all of the probability. Nearly all of these states are the same brain with its water molecules jiggled differently, and nothing a neuron does could tell them apart.

Anything at all

The last ceiling makes no assumptions about what the object is made of. In 1981 Jacob Bekenstein argued, from thought experiments with black holes, that a region of radius R containing energy E can hold only so much information.¹⁸ A precise version, in which entropy and energy are both counted relative to empty space, was later proved within quantum field theory.²⁶

I ≤ 2πRE / (ħc ln 2) ≈ 2.58 × 10⁴³ bits × (mass in kg) × (radius in m)

Here R is the radius of a sphere that encloses the whole object. A brain is about 17 centimetres long, so the sphere needs a radius of about 8.5 centimetres, and with 1.4 kilograms the bound is 3 × 10⁴² bits. Only black holes reach it, and a black hole 8.5 centimetres in radius would weigh nearly ten Earths. Ordinary matter of a brain's mass falls short by about sixteen orders of magnitude, even counting every thermal arrangement. Between the neural count and this ceiling lie nearly 26 orders of magnitude, and they are orders of magnitude in the exponent. (Nº 3 runs these same limits the other way, to price the cheapest physical system that could hold one conscious moment.)

The space is one thing and the path through it is another. Independent budgets limit the path.

The clock. Eighty years is 2.5 billion seconds. Suppose the brain entered a brand-new state every millisecond and never repeated one. A lifetime would visit 2.5 × 10¹² states.

The energy bill. The brain runs on about 20 watts. Landauer's principle says that irreversibly resetting one bit must release at least kT ln 2 of heat, which is 3 × 10⁻²¹ joules at body temperature.¹⁹ (The k ln 2 in it is the entropy of one bit: Nº 17 finds exactly that much in each spin of an infinitely hot collection of spins.) The cost applies only to steps that erase information; a perfectly reversible computer could in principle avoid it, but nothing suggests a brain works that way. Twenty watts therefore pays for at most 6.7 × 10²¹ irreversible bit operations a second, or 1.7 × 10³¹ in a lifetime. The limit is not just theory: in 2012 physicists erased a one-bit memory made of a single microscopic bead held in a laser trap, and as they slowed the erasure, the heat it gave off approached kT ln 2.³⁵ Real neurons are nowhere near it. A 2021 energy budget of the human cortex put the cost of a neuron's computation at about a hundred million times this minimum per bit.³⁶ Grant them perfection anyway, and let every single operation produce a state never seen before: the lifetime total is the same 1.7 × 10³¹ states. Naming one of those takes 104 bits.

The quantum speed limit. That budget covers only the changes the brain pays for. Heat rearranges its molecules for free, so at the finest resolutions the one hard cap is the quantum speed limit: over any long stretch, an isolated object with energy E, measured from its lowest possible state, can pass through at most 2E/h = E/(πħ) fully distinguishable states a second. Only flipping back and forth between two states can go twice as fast; that doubled rate, 2E/(πħ), is the one usually quoted as a count of operations, as in Nº 3.^27,28 Counting the brain's whole mass as energy, E = mc², which is far more than it could ever use, that is about 10⁶⁰ states in 80 years. Naming one of those takes about 200 bits. Naming one state of the whole space takes 6 × 10¹⁶ bits.

What you do with it. When researchers at Caltech gathered decades of measurements of human behaviour, from typing and speech to memory sports and video games, they kept finding about 10 bits per second, against roughly a billion bits per second arriving at the senses.²⁰ Others accept that limit for deliberate thought but argue that the unconscious control of movement runs much faster.³⁰ Ten bits a second for eighty years is 2.5 × 10¹⁰ bits. The record of everything you ever decided would fit in about three gigabytes.

So the share of its own possibilities that a brain ever sees is at most about 10⁶⁰ divided by 10^{1.8 × 1016}. As a decimal, that is a zero, a point, and then some 18 quadrillion more zeros before the first digit that isn't zero.

It isn't memory capacity. Memory needs states that can be written on purpose and read back later. The strength layer is the clearest case, and 4.7 bits times 10¹⁵ synapses is about 600 terabytes, or nearer 150 with the 2 to 3 × 10¹⁴ synapses actually estimated. That is the arithmetic behind the often-quoted figure of roughly a petabyte. Learning also builds and removes synapses, and some new ones last for life, so a few bits of wiring per synapse may count too; that would not change the order of magnitude.^41,42 Usable memory is surely smaller still, because storing one retrievable fact takes many synapses. Psychology has measured it from the other side. In 1986 the psychologist Thomas Landauer, not the physicist of the energy bill, pooled experiments on how much people retain from text, pictures, words and music. People took in about one to two bits a second, and by middle age, he estimated, held around a billion bits: about 125 megabytes, millions of times less than the strength layer.³⁷

It isn't unique to brains. 6.1 × 10¹⁶ bits is about 7.6 petabytes. Any memory that size, some 7,600 one-terabyte drives, has about 10^{1.8 × 1016} states too, and a single one-terabyte drive has 10^{2.4 × 1012}. The count measures how much room a brain has, not what it does with it.

It isn't the number of possible thoughts. Most states in the count are not working minds. They include seizures, comas, and wiring no development could produce. And many different states would behave identically, so the number of distinguishable people is far smaller than the number of distinguishable brains.

It is meant as an upper bound, and a loose one. Two layers are guesses, so this is a judgement, not a proof: the generous choices (wiring free to reach any neuron, 140 transmitters at every synapse, 10¹⁵ synapses) leave several times more room than anything left out is likely to fill. We treated every synapse as free to vary independently of every other. Real brains are built by rules: cell types, layers, genetic programmes, the physics of growth. Every regularity removes states from the count.

The resolution is a choice. Nothing in nature says a brain state stops at synapses. If you believe the mind depends only on spikes and synaptic strengths, the first row of the table is your answer. If you think molecular detail matters, the second row is. Physics supplies the third and fourth rows whatever anyone believes.

What would change it. Four things: a measurement of the slow variables in layer four, which carry the largest guess; a firmer count of human synapses, still uncertain by a factor of five; an account of the glia, which touch many synapses and may hold state of their own; and the state of each neuron's own body, such as which genes are switched on and how excitable it is. At a guess of a few tens of thousands of bits per neuron, that last one would add less than a tenth. Each would shift the total by a modest factor. The upper exponent would stay near 16.

The slogan about stars both undersells the brain and misdescribes it. A brain is a small, warm, finite object, and the number of things it could be is finite too. That number is so large that nothing will ever make use of it. Every brain that has lived, across every moment it lived, has touched a share of its possibilities that rounds to none. A person is one thin path through a space that will stay almost entirely unvisited.