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 Copy Chapter

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 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 Copy Chapter

Approximate numbers that should be consistent between Cloud providers.

† This refers to network leaving your cloud provider, e.g. sending data to S3
from GCP or egress network for sending HTML from AWS to a client.

‡ An additional per cache-fill fee is incurred that costs close to blob storage
write costs (see just below).

7 This is standard pricing among a few logging providers, but e.g. Datadog
pricing is
different and charges $0.1 per ingested logs with $1.5 per 1m on top for 7d
retention.

Furthermore, for blob storage (S3/GCS/R2/...), you're charged per read/write
operation (fewer, large files is cheaper):

Compression Ratios Copy Chapter

This is sourced from a few sources. [3] [4] [5] Note that compression speeds (but
generally not ratios) vary by an order of magnitude depending on the algorithm
and the level of compression (which trades speed for compression).

I typically ballpark that another x in compression ratio decreases performance
by 10x. E.g. we can get a 2x ratio on English
Wikipedia at ~200
MiB/s, and 3x at ~20MiB/s, and 4x at 1MB/s.

Techniques Copy Chapter

• Don't overcomplicate. If you are basing your calculation on more than 6
  assumptions, you're likely making it harder than it should be.
• Keep the units. They're good checksumming.
  Wolframalpha has terrific support if you need a
  hand in converting e.g. KiB to TiB.
• Calculate with exponents. A lot of back-of-the-envelope calculations are
  done with just coefficients and exponents, e.g. c * 10^e. Your goal is to
  get within an order of magnitude right--that's just e. c matters a lot
  less. Only worrying about single-digit coefficients and exponents makes it
  much easier on a napkin (not to speak of all the zeros you avoid writing).
• Perform Fermi decomposition. Write down things you can guess at until you
  can start to hint at an answer. When you want to know the cost of storage
  for logging, you're going to want to know how big a log line is, how many of
  those you have per second, what that costs, and so on.

Resources Copy Chapter

• [1]: https://eli.thegreenplace.net/2018/measuring-context-switching-and-memory-overheads-for-linux-threads/
• [2]: https://blog.tsunanet.net/2010/11/how-long-does-it-take-to-make-context.html
• [3]: https://cran.r-project.org/web/packages/brotli/vignettes/brotli-2015-09-22.pdf
• [4]: https://github.com/google/snappy
• [5]: https://quixdb.github.io/squash-benchmark/
• [6]: https://dl.acm.org/doi/10.1145/1879141.1879143
• [7]: https://en.wikipedia.org/wiki/Hard_disk_drive_performance_characteristics#Seek_times_&_characteristics
• [8]: https://github.com/simdjson/simdjson#performance-results
• [9]: https://github.com/protocolbuffers/protobuf/blob/d20e9a92/docs/performance.md
• [10]: https://www.imperialviolet.org/2010/06/25/overclocking-ssl.html
• [11]: https://github.com/inikep/lzbench
• "How to get consistent results when benchmarking on
  Linux?".
  Great compilation of various Kernel and CPU features to toggle for reliable
  bench-marking, e.g. CPU affinity, disabling turbo boost, etc. It also has
  resources on proper statistical methods for benchmarking.
• LLVM benchmarking tips. Similar
  to the above in terms of dedicating CPUs, disabling address space
  randomization, etc.
• Top-Down performance analysis
  methodology.
  Useful post about using toplev to find the bottlenecks. This is particularly
  useful for the benchmarking suite we have here, to ensure the programs are
  correctly written (I have not taken them through this yet, but plan to).
• Godbolt's compiler explorer. Fantastic resource
  for comparing assembly between Rust and e.g. C with Clang/GCC.
• cargo-show-asm. Cargo extension to allow
  disassembling functions. Unfortunately the support for closure is a bit
  lacking, which requires some refactoring.
• Agner's Assembly
  Guide. An excellent
  resource on writing optimum assembly, which will be useful to inspect the
  various functions for inefficiencies in our suite.
• Agner's Instruction
  Tables. Thorough
  resource on the expected throughput for various instructions which is helpful
  to inspect the assembly.
• halobates.de. Useful resource for low-level
  performance by the author of toplev.
• Systems Performance (book). Fantastic book about analyzing system performance, finding bottlenecks, and understanding operating systems.
• io_uring. Best summary, it links to many
  resources.
• How Long Does It Takes To Make a Context Switch
• Integer Compression Comparisons
• Files are hard