Scope
This calculator implements a polynomial (power-law) bonding curve of the form P(T) = A + B · T^C. Other bonding-curve families are separate models and are not covered here:
- Bancor reserve-ratio: P = R / (S · F), where R is the reserve, S is the supply, F is the reserve ratio.
- Exponential: P(T) = A · e^(k·T) — true exponential growth (base^T), not power-law.
- Logarithmic: P(T) = A + B · ln(T).
- Sigmoid / logistic: cap-limited S-curves.
- Virtual-reserve constant-product (e.g., pump.fun): x · y = k on virtual reserves — not a power curve.
- Friend.tech: a specific quadratic on share count (price_n = n² / 16000 ETH) — a particular case of the power-law family with A=0, B=1/16000, C=2.
How to use
- A (initial price) — base token price at zero supply. Higher A means a more expensive first token.
- B (scale) — curve scaling coefficient. Controls how fast the price grows as supply increases. B uses a logarithmic slider because the useful range spans several orders of magnitude.
- C (steepness) — curve exponent. C < 1 = concave (sub-linear, price flattens as supply grows); C = 1 = linear; C > 1 = convex power law (super-linear supply pressure — steeper and steeper as supply grows). Note: power-law T^C is not exponential growth. True exponential means base^T (e.g., e^(k·T)), which grows faster than any polynomial.
- Max supply — maximum number of tokens on the chart.
- Buy ΔT tokens from T₀ — set a starting supply T₀ and a purchase size ΔT to see the total cost, average price paid, spot price before and after, and slippage.
- The checkpoint table shows spot price, total cost (closed-form integral), and market cap (FDV = P·T) at 0%, 10%, 25%, 50%, 75%, 100% of max supply.
Calculator
Bonding Curve Calculator — Power Law P(T) = A + B·T^C
Buy ΔT tokens from T₀
| Supply | Spot price P(T) | Total cost TC(T) | Market cap (P·T) |
|---|
Reserve-ratio intuition. When A = 0 (pure power curve), TC(T) = B·T^(C+1)/(C+1) and market cap = P(T)·T = B·T^(C+1). So
TC = mcap / (C+1): the pooled reserve is always 1/(C+1) of FDV. In Bancor's constant-reserve-ratio form this maps to F = 1/(C+1) — e.g., linear (C=1) ↔ 50% reserve ratio, quadratic (C=2) ↔ 33%, cubic (C=3) ↔ 25%.Formulas
P(T) = A + B × T^C
- A — initial token price at zero supply ($/token)
- B — scaling coefficient ($/token^(C+1), dimensionally consistent with A + B·T^C yielding $/token)
- C — curve exponent (steepness): C<1 concave, C=1 linear, C>1 convex power law
- T — current token supply (tokens)
- P(T) — spot (marginal) token price at supply T (computed)
TC(T) = ∫₀ᵀ P(t) dt = A·T + B·T^(C+1) / (C+1)
- T — upper integration limit (tokens)
- A, B, C — as above
- TC(T) — total cost to mint the first T tokens (computed, closed form — no numerical integration needed)
Cost(T₀, ΔT) = TC(T₀+ΔT) − TC(T₀)
- T₀ — starting supply before the buy (tokens)
- ΔT — number of tokens being purchased (tokens)
- Cost — total amount paid ($, computed)
AvgPrice(T₀, ΔT) = Cost(T₀, ΔT) / ΔT
- AvgPrice — average price per token paid over the buy (computed, $/token)
Slippage_% = (P(T₀+ΔT) − P(T₀)) / P(T₀)
- Spot slippage — how much the marginal price moved because of the buy (computed, %)
MarketCap(T) = P(T) · T
- MarketCap — fully diluted value at supply T, a.k.a. FDV (computed, $)
- For A = 0 (pure power curve): TC(T) = MarketCap(T) / (C+1), so reserve-ratio F = 1/(C+1).