Rollups

A rollup is a layer-2 blockchain scaling construction in which transactions are executed outside the base blockchain (the layer 1) while the data required to reconstruct them is published to it. By moving computation off-chain and posting compressed transaction data on-chain, rollups increase throughput while continuing to derive their security from the underlying chain rather than from an independent validator set.

Two designs dominate: optimistic rollups, which presume submitted batches are valid and rely on fraud proofs to catch invalid ones, and zero-knowledge (zk) rollups, which accompany every batch with a cryptographic validity proof. Beyond the proof mechanism, rollups are distinguished by an unusual fee structure: because a batch's fixed costs are shared by all transactions inside it, fees can fall as usage grows — within limits.

Optimistic and zero-knowledge rollups

An optimistic rollup executes transactions off-chain and posts the resulting batch data to the base layer — on Ethereum as calldata or as blobs, a dedicated data format that nodes prune after roughly eighteen days. Batches are presumed valid when submitted; correctness is enforced after the fact through multi-round interactive fraud proofs, under which an invalid state commitment can be disputed. A zk-rollup instead submits a validity proof alongside each state commitment. In cost terms the two differ in where their overheads sit: for a zk-rollup the validity proof is a fixed cost incurred even when a batch contains no transactions, while an optimistic rollup carries per-transaction signature data as an additional variable cost.

Data availability

Both designs depend on the base layer to store the data needed to reconstruct the rollup's state, and this transaction data is the largest variable cost of operating a rollup and the primary contributor to rising rollup costs. That expense has motivated hybrid designs — validiums and volitions — that keep transaction data off-chain in search of cheaper average costs. The analytics site L2BEAT accordingly classifies live systems by proof type and data-availability mode, tracking validiums and optimiums separately from rollups proper.

Fee economics

What a rollup user pays bundles two distinct services. Ethereum's developer documentation describes the fee on an optimistic rollup as the cost of writing data to layer 1 plus an operator fee for layer-2 computation. Barnabé Monnot's first-principles analysis draws the same division on the cost side: operators bear layer-2 operating costs, layer-1 data-publication costs — the dominant new cost of the rollup model — and congestion costs on the rollup itself, and must recover them from user fees, extractable value, and issuance, since an operator cannot sustainably run at a loss.

Alex Beckett's analysis of rollup fee economics decomposes the cost of a batch into fixed costs — the state commitment, plus the validity proof for a zk-rollup — and variable costs, chiefly transaction data plus signatures for optimistic rollups. The fee an individual user pays corresponds to the batch's average cost: total cost divided by the number of transactions in the batch. Because fixed costs are amortized over the whole batch, the average falls as the batch grows — so long as the marginal cost of one more transaction sits below the average. In Beckett's worked example, a 500-transaction batch at an average cost of $1 totals $500; adding a transaction with a $0.70 marginal cost lowers the average to $0.9994. On this basis he describes rollups as "the first type of blockchain that can incur positive network effects with regards to transaction fees", in contrast to monolithic chains, where each additional user raises fees for everyone.

The effect has limits. Once marginal cost reaches average cost, the rollup's costs follow a standard short-run cost curve, and past the minimum of that curve each additional transaction pushes fees upward again — the negative network effects of a monolithic chain reappear. And because transaction-data costs are bound to the base layer's finite block space, rollups remain exposed to fee spikes originating on layer 1, especially when the base layer also hosts user-facing applications. Beckett concludes that scalable data-availability layers are fundamental to keeping rollups inexpensive without sacrificing security or decentralization.

Composability across rollups

Each rollup maintains its own state and executes transactions in its own environment. A single transaction therefore cannot atomically span two rollups: moving assets or invoking contracts across them requires bridging or settlement through the base layer. As of mid-2026, L2BEAT tracks roughly twenty-two Ethereum rollups alongside validiums and optimiums, with Arbitrum One the largest at about $17.7 billion in total value secured; it also grades systems on a Stage 0–2 decentralization framework reflecting how far each has reduced reliance on trusted operators. A consequence of this proliferation is that liquidity and application state fragment across many execution environments, and the synchronous, all-or-nothing composability available within a single chain does not extend across the ecosystem as a whole.

Rollups and Radix

Radix addresses the same scaling constraint — often framed as the blockchain trilemma — without a rollup layer, instead scaling the base layer itself through integrated sharding. The network uses a "pre-sharded" design with a fixed, pre-allocated maximum shard space rather than adding shards dynamically, and its Cerberus consensus "braids" validation across shards to enforce system-wide transaction ordering; deterministic shard indexing means transactions from separate accounts involve separate shards and can be processed asynchronously in parallel. On the composability question, radix.wiki's atomic composability page states that a single transaction manifest can chain any number of operations — swaps, loans, deposits, withdrawals — into one all-or-nothing sequence, and that Cerberus braids consensus across every shard a transaction touches, maintaining atomicity across shards, in contrast to sharded systems whose cross-shard operations depend on asynchronous bridges. Rollups and integrated sharding thus represent two responses to the same problem: rollups amortize base-layer costs by moving execution off-chain at the price of fragmenting state across separate environments, while an integrated sharded layer 1 aims to expand execution capacity while preserving a single atomically composable state. For a broader comparison of the two ecosystems' approaches, see Radix vs Ethereum.

References

1. Beckett, Alex (2022). The economics of rollup fees. alexbeckett.xyz (archived via the Internet Archive).
2. Ethereum Foundation. Optimistic Rollups. ethereum.org developer documentation.
3. Monnot, Barnabé (2022). Understanding rollup economics from first principles. The Price of Agency (Substack).
4. L2BEAT. Scaling Summary. l2beat.com, accessed July 2026.