🔵 Curve Finance Internals
Curve is the backbone of stablecoin liquidity in DeFi. Its StableSwap invariant enables swaps between pegged assets with slippage 100–1000× lower than Uniswap. But Curve isn't just an AMM — its vote-escrowed tokenomics created an entire meta-game known as the "Curve Wars," where protocols compete for the right to direct CRV emissions to their pools.
📊 Curve by the Numbers
🔬 How StableSwap Differs
x · y = kSlippage scales with trade size
Works for any asset pair
Poor for pegged assets
x + y = kZero slippage at any size
But pool can be fully drained
Breaks if peg deviates
Near-zero slippage near peg
Graceful degradation if depeg
Amplification parameter A controls the curve shape
⚔️ The Curve Wars — Why Protocols Fight for Gauges
CRV emissions are directed to pools via gauges, and gauge weights are set by veCRV holders. Protocols that need deep stablecoin liquidity (like Frax, Terra, or any new stablecoin) must either accumulate veCRV themselves or bribe veCRV holders to vote for their pool's gauge. This spawned Convex Finance ($CVX), which aggregates veCRV voting power, and Votium, a bribery marketplace — creating a multi-billion dollar governance game.
StableSwap Invariant
The math behind Curve's low-slippage swaps — amplification parameter A and the hybrid constant-sum/constant-product curve
veCRV & Gauge Wars
Lock CRV for voting power, direct emissions, and the meta-game that spawned Convex, Yearn, and an entire governance ecosystem
Gauge Wars & Vote Incentives
Interactive visualization of gauge voting, veCRV lock calculator, voting power decay, and bribe marketplace comparison
Liquidity Pools Deep Dive
Compare StableSwap, Crypto, and Factory pools — interactive simulator for deposits, withdrawals, fee structures, and LP minting
How Curve works in 90 seconds
Curve is a family of automated market makers tuned for assets that should trade near a fixed exchange ratio. The original StableSwap invariant blends a constant-sum and constant-product curve through an amplification parameter A, so trades between USDC, USDT, DAI, FRAX, or LUSD execute with slippage one to three orders of magnitude lower than Uniswap V2 for the same depth. Pools are written in Vyper, swap fees are typically four to ten basis points, and the LP token represents a fungible share of the underlying basket.
Curve V2 — Crypto pools — extends the design to non-pegged baskets such as USDT/WBTC/ETH. The invariant tracks an exponential moving average of the pool's internal prices and continuously repegs the curve toward that EMA, while dynamic fees scale up when the pool is imbalanced. That lets a single pool concentrate liquidity around the moving market price without the LP-management overhead of Uniswap V3 ranges, at the cost of more complex math and higher gas per swap.
The protocol layer on top is veCRV. Locking CRV for up to four years mints veCRV, which votes biweekly on the gauge weights that decide how that period's CRV emissions are split across pools. Protocols that need deep liquidity for a new LST or stablecoin therefore either accumulate veCRV directly or bribe veCRV holders through marketplaces like Votium and StakeDAO. Curve's own native stablecoin, crvUSD, ties this all together with a gentle LLAMMA-based liquidation system that swaps collateral into crvUSD across price bands instead of triggering hard liquidations.
Key concepts
- StableSwap invariant
- The hybrid curve A · n^n · Σx + D = A · n^n · D + D^(n+1) / (n^n · Πx). Near balanced reserves it behaves like a constant sum (almost zero slippage); far from balance it falls back to constant product (graceful degradation). The amplification parameter A is the dial that decides where the transition happens — higher A means flatter near the peg.
- Amplification parameter (A)
- A controls how aggressively the curve sticks to the peg. Curve's mainline 3pool runs A around 200; high-confidence pools like sDAI/USDC have run A above 1000. Higher A boosts capital efficiency at the peg but means a larger share of the pool can be drained quickly if one asset depegs, so risk teams adjust A as confidence in a stablecoin shifts.
- Crypto pools (V2)
- Used for non-pegged baskets like tricrypto USDT/WBTC/ETH. The pool tracks an EMA of the internal price and repegs the StableSwap-style invariant toward it. Dynamic fees rise as the pool drifts from balance, compensating LPs and discouraging adversarial trades. Crypto pools concentrate liquidity around the moving market price without LP-managed ranges.
- veCRV (vote-escrowed CRV)
- Lock 1 CRV for the maximum four years to mint 1 veCRV; shorter locks scale linearly. veCRV holders vote biweekly on gauge weights, claim 50% of trading fees as 3CRV, and earn boosted CRV emissions on their own LP positions. Voting power decays linearly toward zero, so holders must extend or relock to preserve weight.
- Gauges, bribes, and the Curve Wars
- Each whitelisted pool has an on-chain gauge. The biweekly veCRV vote sets gauge weights, which determine each pool's share of the period's CRV emissions. Marketplaces like Votium let protocols pay USD or token bribes per veCRV vote, turning gauge weights into a live auction for liquidity rental — the so-called Curve Wars.
- crvUSD and LLAMMA
- crvUSD is Curve's overcollateralized stablecoin. Instead of triggering Aave/Maker-style hard liquidations, LLAMMA continuously rebalances the collateral into crvUSD across price bands as the collateral falls, then back into collateral as it recovers. Soft liquidation absorbs price moves without the borrower losing the entire margin in a single block.
Why Curve matters
Curve is the price-setting venue for stablecoin-to-stablecoin trades and a primary backstop for LST/ETH liquidity. As of April 2026 the protocol holds roughly $2B in pool TVL spread across Ethereum, Arbitrum, Optimism, Base, Polygon, Fantom, Gnosis, Avalanche, and several appchains, and Curve still routes most of the size flow that aggregators like 1inch and CowSwap send through their stablecoin paths. When a stablecoin depegs or an LST loses its premium, the Curve pool's invariant is usually the first place that re-discovery happens.
Curve also rewrote how on-chain economies coordinate emissions. By turning CRV emissions into gauge votes that any project can buy with bribes, Curve created the first persistent market for liquidity rental. Convex aggregating veCRV, Frax bootstrapping its peg via gauge incentives, and the entire bribe infrastructure (Votium, StakeDAO, Hidden Hand, Pirex) all exist because of that single design choice. crvUSD's LLAMMA liquidation curve and the Crypto pool repegging math then extend the playbook into stablecoins and volatile markets, making Curve more research lab than single product.
Frequently asked questions
- What does the amplification parameter A actually control on Curve?
- A interpolates between a constant-sum (zero slippage, easy to drain) and a constant-product (Uniswap-style) curve. Higher A flattens the invariant near the peg so trades feel almost frictionless when assets are balanced, but it also makes the pool drainable faster if one leg depegs. Curve's most popular stable pools run A between 100 and 2000 depending on collateral confidence.
- How does veCRV voting power actually decay?
- Locking 1 CRV for the maximum four years mints 1 veCRV; shorter locks mint a proportional fraction (e.g. one-year lock = 0.25 veCRV). Voting power then decays linearly toward zero as expiry approaches, so a wallet that locked four years ago has the same power as a wallet that just locked one year. To preserve voting weight a holder must extend the lock or relock fresh CRV.
- Why are CRV emissions split via gauges?
- Each pool has an LP gauge that streams CRV emissions to LPs in proportion to the gauge's weight, and weights are reset every two weeks by veCRV vote. Protocols that need deep liquidity for their stablecoin or LST can either accumulate veCRV themselves or pay bribes through Votium and StakeDAO to redirect emissions to their pool — that incentive game is the Curve Wars.
- What is crvUSD and how does it relate to LLAMMA?
- crvUSD is Curve's native overcollateralized stablecoin. Instead of clean liquidation auctions, the LLAMMA AMM continuously swaps a borrower's collateral into crvUSD across a range of price bands as the collateral price falls, then swaps it back as the price recovers. The result is gradual soft liquidation rather than a single hard-liquidation event.
- How do Crypto pools differ from StableSwap pools?
- Curve's Crypto pools (V2) use a dynamic-peg invariant that lets non-pegged assets like ETH and WBTC trade in a single pool with concentrated, internally-rebalanced liquidity. The pool tracks an exponential moving average of the price, repegs the curve toward that EMA, and applies dynamic fees scaled by the pool's distance from balance. It is what makes the tricrypto USDT/WBTC/ETH pool viable.
- What is Convex and why did it dominate the Curve ecosystem?
- Convex Finance permanently locks user-supplied CRV as veCRV and issues cvxCRV in return. By aggregating veCRV, Convex captured majority influence over Curve gauge votes, which let it offer LPs boosted CRV rewards on top of CVX emissions without the LPs themselves locking CRV. Vote-bribery now flows largely through Convex's vlCVX layer.
- How big is Curve in DeFi today?
- As of April 2026 Curve carries roughly $2B in pool TVL across Ethereum, Arbitrum, Optimism, Base, Polygon, Fantom, Gnosis, Avalanche, and several appchains, while crvUSD circulates at a few hundred million. Curve still routes the lion's share of stablecoin-to-stablecoin volume on aggregators like 1inch and CowSwap, especially for size above a few million dollars.