Use a hypothetical purchased-equipment price of $100,000 for a 1,000-US-gallon unit to estimate two comparable 2,000-US-gallon units at the same price date. This is a mathematical benchmark, not a market quote.
1. Calculator Inputs
Select the units below before entering the numbers. These are fixed benchmark inputs for checking the calculator.
| Calculator field | Value | Unit / setting |
|---|---|---|
| Reference cost, C₁ | 100,000 | USD |
| Reference cost basis | Purchased equipment cost | |
| Sizing parameter | Volume | |
| Reference size, Q₁ | 1,000 | US gal |
| Target size per unit, Q₂ | 2,000 | US gal |
| Number of identical target units | 2 | |
| Exponent method | Six-tenths rule · n = 0.60 | |
| Adjust for price date using cost indices | Disabled |
2. Step-by-step Math
Calculate the per-unit size ratio
r = Q₂/Q₁ = 2,000 / 1,000 = 2
Both sizes use US gallons, so the unit cancels. The target size is 2,000 gallons per unit; quantity is handled separately.
Apply the assumed exponent
C₂ = C₁ × (Q₂/Q₁)^n Scale factor = 2^0.60 ≈ 1.52 C₂ = $100,000 × 1.515716566510 C₂ = $151,571.656651 per unit
The 0.60 exponent is a screening assumption. It is not a validated equipment-specific cost correlation.
Multiply by the number of units
Total = quantity × per-unit cost Total = 2 × $151,571.656651 Total = $303,143.313302 Per-unit increase = (1.515716566510 − 1) × 100 Per-unit increase ≈ 51.6%
Do not combine the two target units into one 4,000-gallon unit before scaling. That is a different equipment configuration.
Check exponent sensitivity
n = 0.50: total = 2 × $100,000 × 2^0.50 = $282,842.71 n = 0.60: total = 2 × $100,000 × 2^0.60 = $303,143.31 n = 0.70: total = 2 × $100,000 × 2^0.70 = $324,900.96
These scenarios vary only the exponent. They are not a statistical confidence interval or a complete estimate uncertainty range.
3. Compare Your Answers
Keep full precision during the calculation. The calculator may display fewer digits; compare answers rounded to three significant figures; retain unrounded intermediate values.
| Result | Expected answer | Your answer |
|---|---|---|
| Size ratio | 2 | __________ |
| Cost multiplier | 1.52 | __________ |
| Per-unit cost | $151,571.66 | __________ |
| Total cost for two units | $303,143.31 | __________ |
| Price-index multiplier | 1 (adjustment disabled) | __________ |
Second check
Switch Exponent method to Linear scaling. With n = 1, the per-unit estimate becomes $200,000 and the two-unit total becomes $400,000. This provides a simple independent check of quantity handling.
4. Assumptions and Method
The reference price, capacities and exponent are hypothetical. Both units must have comparable material, pressure rating, design, scope, currency and price date. Purchased-equipment cost does not automatically include freight, installation, piping, controls, engineering or contingency. No current price index is assumed.
Equation definitions and implementation: Equipment Cost Scaling Calculator. See also calculation methodology and other worked examples.