Concept

Six-tenths rule

Overview

The six-tenths rule estimates the cost of equipment at a new size by scaling a known cost at a reference size, raising the size ratio to an exponent of roughly 0.6. It captures economy of scale: doubling capacity costs less than double, because cost tracks surface-like quantities while capacity tracks volume-like ones.

Body

A power-law scaling between two sizes of the same equipment:

C₂ = C₁ · (S₂ / S₁)ⁿ

C₁ is the known cost at reference size S₁; C₂ the estimate at new size S₂; n the scaling exponent (the “six-tenths,” n ≈ 0.6 on average). S is any capacity/throughput measure (volume, area, power, mass flow, duty), with S₁ and S₂ in the same unit; C₁ and C₂ on the same basis — currency, cost year, battery-limits scope (see Capex).

Why ~0.6. Equipment cost is often set by the material in a shell or vessel, scaling with surface area (~length²), while capacity scales with volume (~length³). The ratio of exponents is 2/3 ≈ 0.67; empirical fits cluster a little below that.

The exponent is class-specific. 0.6 is an aggregate default. Each class — compressors, exchangers, vessels, pumps, reactors — has its own, listed in Sizing scalars. Use the class value when available; 0.6 is the fallback.

Where it sits. The rule scales a single item once sized; scaled item costs then aggregate toward Total capex. Splitting capacity across multiple identical trains is the separate question of Numbering up / down.

Limits & typical error

• Valid only near the reference size — the power law is a local fit; the further S₂ is extrapolated, the more it degrades as the true curve bends away from one exponent.
• Exponent sensitivity is mild over a normal range — across the 0.5–0.7 band, a 3× size change moves cost only ~15%, so the estimate’s error is dominated by the reference cost and the size basis, not the exponent.
• But a wrong exponent compounds with the size ratio — exponent error enters as (S₂/S₁)^Δn, negligible at 2× but material at 10× or 100×.
• It inherits all uncertainty in the reference cost — scaling is multiplicative: a 25%-off C₁ gives a 25%-off C₂ before any exponent error (see reference / comparable process).
• The size basis of S₁ and S₂ must match — scaling on volume when the reference was quoted on throughput, or nameplate vs. operating, silently breaks the rule.
• Out-of-range is a discontinuity, not a smooth curve — past a class’s maximum size a single larger unit may not exist; cost shifts to a numbering-up regime, with no warning at the boundary.
• Like-for-like only — same equipment type, configuration, and materials; scaling across a metallurgy or pressure-rating change folds an unrelated cost step into a size effect.

Mini-example

Scaling a compressor for a green-ammonia plant. A centrifugal compressor of the synthesis-loop type has a known purchased cost of $2.0M at a 5 MW reference; the design calls for 8 MW — a modest 1.6× step, comfortably in range and like-for-like. Taking n = 0.62 for centrifugal compressors (from Sizing scalars):

C₂ = $2.0M · (8 / 5)^0.62  =  $2.0M · 1.34  ≈  $2.7M

~$2.7M — and because the size ratio is small, the answer barely moves if the exponent is 0.58 or 0.66, confirming the reference cost is the thing worth getting right.

Edge case: scale that same 5 MW reference to an 80 MW machine (16×) and the rule returns a single-unit cost for a compressor that likely exceeds any standard frame — the point where the power law stops applying and a numbering-up arrangement becomes the right model.

See also

• Sizing scalars (by equipment class)
• Equipment sizing
• Capex
• Total capex (battery-limits → total plant)
• Numbering up / down
• Reference / comparable process