Block Subsidy

The Bitcoin block subsidy is the amount of new Bitcoin created with each block. It follows a predictable mathematical formula that halves every 210,000 blocks, creating Bitcoin's fixed supply schedule.

The block reward is what the miner receives for mining a valid block: the block subsidy (new bitcoin created) plus the transaction fees from all transactions included in the block. Over time, the subsidy shrinks (halving every 210,000 blocks) and fees will make up a larger share of miner revenue.

Mathematical Formula

Block Subsidy = 50 / (2^halvings)

Where:
  halvings = floor(block_height / 210,000)

Bitcoin Core Implementation

In Bitcoin Core (validation.cpp), the subsidy is calculated using bit shifting for efficiency:

CAmount GetBlockSubsidy(int nHeight, const Consensus::Params& consensusParams)
{
    int halvings = nHeight / consensusParams.nSubsidyHalvingInterval;
    // Force block reward to zero when right shift is undefined.
    if (halvings >= 64)
        return 0;

    CAmount nSubsidy = 50 * COIN;
    // Subsidy is cut in half every 210,000 blocks which will occur approximately every 4 years.
    nSubsidy >>= halvings;
    return nSubsidy;
}

The right bit shift (>>=) divides by 2 for each halving, which is equivalent to the mathematical formula but more efficient.

Code Implementation

Example Calculations

Block 0 (Genesis Block):

halvings = 0 / 210,000 = 0
subsidy = 50 / (2^0) = 50 BTC

Block 840,000 (Fourth Halving):

halvings = 840,000 / 210,000 = 4
subsidy = 50 / (2^4) = 3.125 BTC

The total Bitcoin supply follows a geometric series that converges to exactly 21 million BTC:

Total Supply = 210,000 blocks × 50 BTC × (1 + 1/2 + 1/4 + 1/8 + ...)
             = 210,000 × 50 × 2
             = 21,000,000 BTC

Why 21 Million?

The limit arises from:

• Initial subsidy: 50 BTC
• Halving interval: 210,000 blocks
• Geometric series sum: 50 × 210,000 × 2 = 21,000,000

After approximately 64 halvings (around year 2140), the subsidy drops below 1 satoshi and becomes zero.

Calculate Total Supply Up to Block

Find Next Halving

The total block reward consists of two parts:

Total Block Reward = Block Subsidy + Transaction Fees

As the subsidy decreases, transaction fees become increasingly important for mining economics and network security.

Bitcoin's inflation rate decreases predictably over time:

Annual Inflation = (Blocks per Year × Subsidy) / Total Supply × 100%

Example (2024):
- Blocks per year: ~52,560 (365.25 × 24 × 6)
- Subsidy: 3.125 BTC
- New BTC per year: ~164,250 BTC
- Total supply: ~19,700,000 BTC
- Inflation rate: ~0.83%

Predictability

• Anyone can calculate the exact supply at any block height
• No central authority can change the schedule
• Requires network consensus to modify

Scarcity

• Fixed maximum of 21 million BTC
• Decreasing issuance over time
• Eventually deflationary (lost coins exceed new issuance)

Security Transition

• Early: Security funded primarily by subsidy
• Current: Mix of subsidy and fees
• Future: Security must come from fee market

Subsidy (BTC)
      │
50    │████████
25    │        ████████
12.5  │                ████████
6.25  │                        ████████
3.125 │                                ████████
1.5625│                                        ████████
      │
      └────────────────────────────────────────────────→ Blocks
       0      210k    420k    630k    840k    1050k

• Bitcoin Core: validation.cpp: Subsidy calculation in source code
• Bitcoin Wiki: Controlled Supply: Detailed supply schedule
• Clark Moody Dashboard: Live supply statistics