1. Reference equipment and target size
Start with the price of one reference unit. Enter the target size per unit; the quantity is applied separately.
Both sizes must describe the same physical parameter. Unit changes convert existing values.
The result retains your reference cost basis. Choosing “installed” does not add installation. Currency selection changes labels only.
2. Choose the scaling exponent
An exponent is not a Lang installation factor. Use an exponent for this equipment type, sizing parameter, and size range.
The reference item above is quote 1. Enter quote 2 for one comparable unit at the same price date. The optional index adjustment below is applied after fitting, from that shared date to the target date.
Use the same index series and base period for both values. Defaults 500 and 600 are illustrative, not published historical or current index values. Enter verified indices appropriate to the cost scope.
3. Estimated equipment cost
Enter your reference and target sizes, then calculate.
| Calculation step | Value |
|---|
Exponent sensitivity
Compare the selected exponent with n − 0.10 (minimum zero) and n + 0.10. These are scenarios, not uncertainty bounds. When scaling down, a higher exponent gives a lower cost.
| Exponent scenario | Total for target units |
|---|
Equations and a worked example
C₂ = C₁ × (Q₂ / Q₁)ⁿ × (I₂ / I₁)
Total = N × C₂
n = ln(Cᵦ / C₁) / ln(Qᵦ / Q₁)
C₁ is the known cost of one item, Q₁ its size, Q₂ the target size per item, n the scaling exponent, and N the target unit count. The index ratio is 1 when price-date adjustment is off. The fitted-exponent equation uses a second comparable quoted cost Cᵦ and size Qᵦ.
Example: a 10 m³ item costs $100,000. For one 20 m³ item with n = 0.60, the size multiplier is 2⁰·⁶ ≈ 1.515717, giving $151,571.66 before time adjustment. Illustrative indices of 500 and 600 give a 1.20 multiplier and $181,885.99 per target unit. Two such units cost $363,771.98 before any additional scope.
Choose a defensible exponent and sizing parameter
Use vendor quotes or a documented correlation for closely matching equipment. Record its equipment type, construction material, design conditions, sizing parameter, size limits, cost date, and included scope. Use 0.60 as a preliminary assumption when better data are unavailable, then test sensitivity.
| Equipment | Possible sizing parameter | What to hold comparable |
|---|---|---|
| Tank or vessel | Internal volume | Geometry, material, pressure rating, internals, fabrication constraints |
| Heat exchanger | Heat-transfer area | Exchanger construction, material, pressure rating; duty alone is insufficient without thermal design |
| Pump or compressor | Rated power, or the parameter specified by the correlation | Machine type, pressure/head, stages, drive, and package scope |
| Other process equipment | Throughput or a documented design parameter | Same service, technology, and valid correlation range |
No generic equipment exponent is automatically assigned by the sizing-parameter selector. Published exponents can use different parameters and ranges; choosing “volume” does not establish that 0.60 applies to your vessel.
Scaling versus duplication
For N identical items, scale the cost of one target item and multiply by N. Do not put the combined capacity of all items into the size ratio and also multiply by N. Standby equipment, shared utilities, and package discounts need separate scope estimates.
For example, two unchanged 10 m³ units cost twice the reference-unit price in this model. One 20 m³ unit follows the selected size exponent instead.
Price-date adjustment
An index ratio changes the price basis over time. It does not automatically adjust for currency, geography, special alloys, installation, or altered specifications. Choose a series appropriate to the reference scope and use consistent periods and rebasing.
Purchased, delivered, and installed prices have different inclusions. This calculator preserves whichever scope you enter; it adds no installation or contingency allowance.
Limits and next steps
Use this for preliminary comparisons between similar items. Large changes in size can require another design, multiple trains, or different fabrication methods. Very small equipment can have a price floor that a power law misses. A fitted exponent from two quotes is sensitive to discounts and scope differences.
When you need a plant-level estimate, use the Plant Construction Cost Estimator after reconciling the equipment-cost basis with the chosen plant factor. Scaling exponents and installation multipliers serve different purposes.
Method references
- AACE RP 59R-10 public sample: capacity factoring, cost-index ratios, and extrapolation limitations. The fitted exponent here follows algebraically from C₂/C₁ = (Q₂/Q₁)ⁿ.
- Foundations of Chemical and Biological Engineering I: Purchased Equipment Cost: capacity and time adjustment equations. Its illustrative exponent/index tables are not loaded as commercial cost data.
- NETL: Capital Cost Scaling Methodology, Revision 4: an example of equipment/account-specific scaling parameters, exponents, and ranges.