How to use
- Initial reward / month — token volume paid out in the first month. Decreases over time following the half-life formula.
- Half-life (continuous decay) — number of months after which the reward is cut in half. Shorter half-life = faster decay.
- Total supply (cap) — maximum emission volume. When cumulative emission reaches the cap, rewards stop.
- Horizon — modeling period in months.
- Four cards show: total emitted tokens, percentage of cap, emission rate in the last month, and the theoretical infinite-horizon sum. The chart shows cumulative (purple) and monthly (red) emission.
Scope: exponential decay only
This calculator implements continuous exponential decay: R(t) = R₀ · 0.5^(t/H), where H is the half-life in months. It is distinct from Bitcoin-style discrete step halving, where the reward is constant between halving events and then drops in a single step at a fixed block height. It also does not cover constant emission (fixed reward every block) or linear decay (reward falls by a fixed amount each period). Those are separate emission models — see the parent article Reward Emission for a comparison.Calculator
Exponential Emission Calculator
Tokens emitted
0
% of supply
0%
Emission rate (last month)
0%
Infinite-horizon sum
0
Cumulative emission (left axis, tokens)
Monthly emission (right axis, tokens)
Emission rate = R(m) / Total(m−1) — assumes the token has no pre-mine (all supply comes from emissions). For tokens with pre-mine or team allocations, true inflation is lower.
Formulas
R(m) = R0 × 0.5^((m−1)/H)
- R(m) — reward in month m, tokens (computed)
- R0 — initial reward in month 1 (tokens)
- H — half-life in months (continuous decay constant)
- m — month number
- Note: this is continuous exponential decay, not step halving. In step halving (Bitcoin-style) the reward is constant for H months and then drops by 50% in one step; here it drops smoothly every month.
Total(m) = Σ R(i), i = 1..m, Total ≤ Cap
- Total(m) — cumulative emission by month m (computed)
- Cap — maximum emission volume (tokens)
- If Total + R(m) > Cap, the reward is truncated to Cap − Total (visible on the chart as a “Cap reached at month N” marker)
Rate(m) = R(m) / Total(m−1)
- Rate(m) — emission rate in month m relative to cumulative emission (computed)
- Displayed as a percentage and labelled “Emission rate (last month)”
- Equals inflation only if the token has zero pre-mine; for tokens with pre-mine or team allocations, true inflation is lower because the denominator (circulating supply) is larger
Total_∞ = R0 / (1 − 0.5^(1/H))
- Total_∞ — theoretical infinite-horizon sum of emissions with no cap (computed)
- Approximately equal to R0 · H / ln 2
- If Total_∞ < Cap, the cap is unreachable under the current parameters