Bitcoin Total Supply

Bitcoin’s supply isn’t capped by a flag. It’s capped by the subsidy function every node runs against every block. The canonical form lives in GetBlockSubsidy:

nSubsidy = 50 BTC; nSubsidy >>= floor(height / 210000); return nSubsidy.

Every 210,000 blocks the right-shift effectively halves the reward. After 33 such shifts the satoshi-level value is zero and the subsidy stops. The geometric series that this produces converges to 20,999,999.9769 BTC, not 21,000,000 — because the shifts are integer truncating and the rounded-down satoshis compound. A coinbase transaction whose payout exceeds the function’s return is rejected by every full node. That’s the cap.

Per-epoch issuance is 210,000 × rewardn where rewardn = floor(5,000,000,000 / 2n) satoshis. Sum across n = 0…32 and the result is exactly 2,099,999,997,690,000 satoshis — the headline 21,000,000 BTC minus a 2,310,000-satoshi shortfall that the integer arithmetic accumulates over the 33 halvings.

The first four epochs do most of the work: 50 + 25 + 12.5 + 6.25 BTC per block, summed across 210,000 blocks each, accounts for 93.75% of the asymptote inside the first sixteen years. The remaining 6.25% is paid out across the next hundred-plus years, halving each epoch until the per-block reward shrinks to a single satoshi.

Plug a calendar date into the same GetBlockSubsidy sum and you get the protocol-level supply on that date. The figures below assume each epoch lasts a flat four calendar years; in practice block intervals have averaged closer to 9.6 minutes and historic halvings have arrived a few weeks early. The active epoch’s row is therefore a planning estimate, not a block-height countdown.

Issued supply isn’t the same as accessible supply. The most-cited estimate is a 2017 study putting the permanently-unrecoverable share at 2.78 to 3.79 million BTC — built on the heuristic that coins untouched for five years or more are likely lost. Subsequent work has widened the range and challenged the methodology. Long-dormant isn’t the same as lost: cold-storage generations, inheritance reactivations, and quiet long-horizon holders all break the “five years untouched” rule, and a single 2024 movement of an eleven-year-old Satoshi-era cohort can compress the headline figure by 50,000 BTC in a day.

The figure published here is the issued one, not a guess at the accessible one. An analytical alternative values each unspent output at its last-moved price rather than treating dormancy as binary; the realised-cap framework on MVRV is the most legible read. A single point estimate for lost coins is the wrong object to want.

The last block to carry any subsidy at all lands at height 6,929,999, sometime around the year 2140. Long before that, the subsidy shrinks below economic relevance: by epoch 12 (mid-2050s) it’s under 0.025 BTC per block; by epoch 20 (late 2080s) it’s under 0.0001 BTC per block. The transition to a fee-funded security budget therefore plays out across decades, not centuries. The live read on how that’s going lives on Daily Fees — specifically the share of miner revenue paid in fees rather than subsidy, which already crosses 100% on a handful of fee-spike days each year.

Block-time drift. The supply curve is denominated in blocks, not days. The active-epoch row in the projection table assumes a flat four-year era; the protocol allows the boundary to land a few weeks either side, depending on hash rate and difficulty trajectory. The completed-epoch rows (0–3) are exact; only the live row floats.

Unmined fractional satoshis. A few historical blocks were mined with a coinbase that paid less than the full subsidy — one notable example is block 124,724 in 2011, whose miner claimed only 49.99999999 BTC of the 50 BTC subsidy and forfeited the block’s ≈0.01 BTC of fees. Tiny shortfalls of this kind reduce the actual circulating figure below the programmed maximum by a few dozen BTC. The asymptote remains the same; it just isn’t fully consumed.

Pending coinbase maturity. Coinbase outputs are unspendable for 100 blocks. Most circulating-supply trackers ignore this; we don’t correct for it either. Treat the live circulating figure as ‘issued’, not ‘spendable today’.

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