napkin-math

Napkin Math

The goal of this project is to collect software, numbers, and techniques to quickly estimate the expected performance of systems from first-principles. For example, how quickly can you read 1 GB of memory? By composing these resources you should be able to answer interesting questions like: how much storage cost should you expect to pay for logging for an application with 100,000 RPS?

The best introduction to this skill is through my talk at SRECON.

The best way to practise napkin math in the grand domain of computers is to work on your own problems. The second-best is to subscribe to this newsletter where you'll get a problem every few weeks to practise on. It should only take you a few minutes to solve each one as your facility with these techniques improve.

The archive of problems to practise with are here. The solution will be in the following newsletter.

Numbers

Below are numbers rounded for memorization, not faux precision. The rows this repo can currently refresh on a single host were re-measured and revalidated on fresh GCP c4-standard-48-lssd instances on March 8, 2026 (Intel Xeon 6985P-C, 48 vCPU / 24 physical cores, 180 GB RAM, Ubuntu 22.04.5 LTS).

Note 1: Some throughput and latency numbers don't line up, this is intentional for ease of calculations.

Note 2: Take the numbers with a grain of salt. E.g. for I/O, [fio][fio] is the state-of-the-art. I am continuously updating these numbers as I learn more to improve accuracy and as hardware improves.

†: "Fast serialization/deserialization" is typically a simple wire-protocol that just dumps bytes, or a very efficient environment. Typically standard serialization such as e.g. JSON will be of the slower kind. We include both here as serialization/deserialization is a very, very broad topic with extremely different performance characteristics depending on data and implementation.

For the active Criterion suite, run ./run --bench napkin_math to get the right optimization levels and Linux tuning. You won't get the right numbers when you're compiling in debug mode. The wrapper already uses sudo internally. On locked-down cloud images, run sudo sysctl -w kernel.perf_event_paranoid=-1 once before invoking it. You can help this project by adding new suites and filling out the blanks.

Note: The active benchmark path today is Criterion.rs in benches/. src/main.rs is still the older ad hoc harness and remains the source of truth for the benches that have not been fully migrated and revalidated yet. The current Criterion suite now includes blob_storage, memory_read, memory_random, hash, syscall, sort, serialization, compression, and compressed_memory_read. The current SSD rows were refreshed from the older harness with NAPKIN_BENCH_FILE pointed at a RAID0 local-SSD mount. The compressed_memory_read Criterion bench is a BitPacker integer-unpack microbenchmark; it should not be used to rewrite the generic [11] compression/decompression rows above. The new serialization and compression Criterion groups are workload-specific and are not yet wired into the generic README rows above. The new blob_storage Criterion group is opt-in and credentialed: set NAPKIN_GCS_BUCKET and/or NAPKIN_S3_BUCKET. Both the GCS and S3 paths now use the AWS S3 SDK. The GCS side talks to the GCS XML interoperability endpoint and requires NAPKIN_GCS_ACCESS_KEY plus NAPKIN_GCS_SECRET_KEY. The S3 side uses the local AWS profile in NAPKIN_S3_PROFILE (default tpuf-test) plus NAPKIN_S3_REGION (default us-west-2). The concurrent get_offsets and put_multipart paths explicitly fan out onto a multi-thread Tokio runtime, so they can get close to the host NIC limit when the range count / object count is high enough. On March 9, 2026, same-region 1 GiB single-stream GETs landed at about 95 MiB/s on S3 (m6id.12xlarge in us-west-2a) and about 190-200 MiB/s on GCS XML (c4-standard-48-lssd in us-central1-c). On the same machines, explicit concurrent range GETs reached about 2.0 GiB/s on S3 and about 4.9 GiB/s on GCS, while multipart PUTs reached about 1.8-1.9 GiB/s on S3 and about 3.3 GiB/s on GCS. AWS's own S3 guidance suggests budgeting about 85-90 MB/s per concurrent request when saturating a 10 Gbps instance, which matched the measured S3 single-stream result closely. The old 500 MiB/s single-stream blob GET row above did not reproduce on either provider, so it has been revised down to a conservative generic 100 MiB/s. The current blob-storage work has revalidated throughput much more than first-byte latency; the 50 ms / 150 ms latency cells above should still be read as rough heuristics until a dedicated small-object / time-to-first-byte probe is added. There is now a dedicated small-object latency probe in src/bin/s3_latency.rs. Run ./script/blob-latency s3 or ./script/blob-latency gcs to sweep get, put, if_none_match, and put_if_match across the default 8 KiB .. 8 MiB size ladder, except if_none_match, which now defaults to a single 128 KiB row because its latency was effectively flat across the small size sweep. Override NAPKIN_BLOB_LATENCY_OPS, NAPKIN_BLOB_LATENCY_SIZES, and NAPKIN_BLOB_LATENCY_IF_NONE_MATCH_SIZES when you want a smaller or provider-specific run. The latency probe now defaults to a per-row wall-clock budget of 300 seconds, collecting as many samples as fit in that time. Tune that with NAPKIN_BLOB_LATENCY_ROW_SECONDS; optionally cap it with NAPKIN_BLOB_LATENCY_SAMPLE_CAP (or the older NAPKIN_BLOB_LATENCY_SAMPLES alias) when you want shorter count-limited experiments instead. The list op now seeds a larger namespace by default (100k keys) and measures one randomized 1000-key page per sample via start_after, rather than repeatedly scanning the same small fixed prefix. Tune that shape with NAPKIN_BLOB_LATENCY_LIST_NAMESPACE_KEYS, NAPKIN_BLOB_LATENCY_LIST_KEYS, and NAPKIN_BLOB_LATENCY_LIST_SEED_CONCURRENCY. If you also want the old whole-namespace walk, add list_full_scan to NAPKIN_BLOB_LATENCY_OPS. For aligned range-read latency, ./script/blob-random-range-latency measures the 128 KiB-aligned shape and ./script/blob-random-range-latency-8m measures the 8 MiB-aligned shape over the same 128 x 1 GiB object pool. ./script/blob-random-range-latency-8m-multipart seeds those 1 GiB source objects via multipart upload with 8 MiB parts, then measures 8 MiB-aligned reads against those multipart boundaries. memory_read now emits explicit No SIMD and SIMD variants in Criterion, but the README intentionally collapses them to one single-thread row and one threaded row for memorability.

I am aware of some inefficiencies in this suite. I intend to improve my skills in this area, in order to ensure the numbers are the upper-bound of performance you may be able to squeeze out in production. I find it highly unlikely any of them will be more than 2-3x off, which shouldn't be a problem for most users.

Cost Numbers

Approximate numbers that should be consistent between Cloud providers.