Power-sizing model

The power-sizing model estimates the cost of a new project from a known cost of a similar project at a different size. It assumes economies of scale, so cost grows more slowly than size:

Power-sizing cost estimate $C=a{S}^x$ with $x=0.7$; concavity captures economies of scale.

$C_a=C_b{\left(\frac{S_a}{S_b}\right)}^x$

where $C_b$ is the cost of the known reference project at size $S_b$, $C_a$ is the cost being estimated at the new size $S_a$, and $x$ is the cost-capacity exponent (also called the cost-size or power-sizing factor).

The exponent $x$ controls how cost scales with size. Three regimes:

• $0<x<1$ — economies of scale. Doubling size multiplies cost by $2^x<2$, so cost per unit of capacity falls as size grows. This is the regime for nearly all engineering equipment.
• $x=1$ — no scale effect. Cost is linear in size; cost per unit of capacity is constant.
• $x>1$ — diseconomies of scale. Cost grows faster than size, usually because you’ve crossed a capacity threshold (different foundation, different design code, higher steel grade, more complex controls).

For chemical-process equipment, $x\approx 0.6$ is so common that the rule is often called the “six-tenths rule”: doubling the size multiplies cost by $2^{0.6}\approx 1.52$, not by 2. Larger equipment is cheaper per unit of capacity because shells, foundations, and instrumentation don’t scale linearly with throughput.

Typical exponents (rough): heat exchangers $\sim 0.6$, storage tanks $\sim 0.6$, compressors $\sim 0.8$, refineries $\sim 0.65$. Buildings tend toward $0.7$, bigger buildings costing less per square foot for the same reason. Civil works (roads, pipelines) tend higher, closer to $0.8$-$0.9$, because cost is more closely tied to length.

Use power-sizing when you have a reliable cost data point for a similar item at a different size, and the historical exponent for the category is known or can be looked up. Expect budgetary-grade accuracy (±10-20%).

Extrapolating across more than a factor-of-3 or so in size, the exponent itself may shift. Past some scale point you may need different equipment topology entirely, and the cost curve takes a step. Use power-sizing within the regime it was fit to.

See also Parametric cost estimation and the overall hierarchy in Cost estimate classes.