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 Equation

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

Halving Schedule

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

Total Supply

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.

Utility Functions

Calculate Total Supply Up to Block

Find Next Halving

Block Reward Components

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.

Inflation Rate

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%

Key Properties

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

Visual Representation

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

Resources

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