---
title: "Roofline attainable-performance bound"
description: "Bounds attainable kernel performance by whichever ceiling is lower: compute throughput or data-movement throughput."
canonical_url: "https://fanout.sh/labs/math-decoder/formula/roofline-performance-bound"
md_url: "https://fanout.sh/labs/math-decoder/formula/roofline-performance-bound.md"
last_updated: "2026-08-09"
access: "public"
---

# Roofline attainable-performance bound

Bounds attainable kernel performance by whichever ceiling is lower: compute throughput or data-movement throughput.

## Public overview

Attainable performance equals the minimum of peak compute performance and memory bandwidth times arithmetic intensity.

A kernel runs no faster than its compute hardware or its ability to feed data, whichever limit is reached first.

Minimum is the main verb: performance is capped by the lower of two independently calculated roofs.

The Roofline model is an upper-bound diagnostic, not a latency prediction; overheads and imperfect utilization can place real performance below the roof.

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