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, using the assumption that economies of scale make cost grow more slowly than size:

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

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, and three regimes matter:

• $0<x<1$ — 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 cost 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. The result is generally budgetary-grade accuracy (±10-20%).

If you’re 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.

For other estimation techniques in the same toolbox, see Unit cost estimation, Parametric cost estimation, Cost index, and the overall hierarchy in Cost estimate classes.