3D Printing Sensitivity Analysis Formula
Learn how material price, print time, machine cost, and failures are combined to estimate the expected cost of a successful 3D print.
This calculator compares the expected cost per successful print at baseline settings with a what-if scenario. It estimates the cost of one attempt, then adjusts it for expected failed attempts so changes in effective speed, filament price, and hourly machine cost can be evaluated consistently.
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Scenario Expected Cost per Successful Print
Where:
First calculate the material and machine cost for one scenario attempt. Then divide that attempt cost by the expected success rate to allow for the cost of repeat attempts.
Variables Explained
| Variable | What It Means | Unit |
|---|---|---|
| filamentWeight - Filament used per successful print | Estimated material weight for one completed print, excluding failed attempts. | g |
| filamentPricePerKg - Baseline filament price per kilogram | Purchase price of the printing material before the scenario adjustment. | currency |
| filamentPriceChange - Filament price change | Percentage increase or decrease applied to the baseline material price. | percent |
| basePrintHours - Baseline print time | Machine run time for one completed print at the current settings. | hours |
| printSpeedChange - Effective print speed change | Percentage change in effective print speed; a positive value reduces estimated print time inversely. | percent |
| machineRate - Baseline machine cost per hour | Hourly operating cost included in the estimate. | currency |
| machineRateChange - Machine hourly rate change | Percentage increase or decrease applied to the hourly machine cost. | percent |
| failureRate - Expected print failure rate | Percentage of attempts expected to fail and require another attempt. | percent |
Step-by-Step Calculation
Calculate baseline material cost
Convert material weight from grams to kilograms, then multiply by the baseline price per kilogram.
baselineMaterialCost = (filamentWeight / 1000) * filamentPricePerKg
Calculate baseline machine cost
Multiply the baseline machine run time by the hourly machine cost.
baselineMachineCost = basePrintHours * machineRate
Allow for baseline failures
Divide the cost of one attempt by the expected success rate to estimate cost per successful print.
baselineExpectedCost = (baselineMaterialCost + baselineMachineCost) / (1 - failureRate / 100)
Adjust scenario price and machine rate
Apply the selected percentage changes to material price and machine cost per hour.
scenarioFilamentPrice = filamentPricePerKg * (1 + filamentPriceChange / 100); scenarioMachineRate = machineRate * (1 + machineRateChange / 100)
Calculate scenario print time
A speed increase reduces time inversely. For example, 20% faster means dividing time by 1.20.
scenarioPrintHours = basePrintHours / (1 + printSpeedChange / 100)
Calculate scenario expected cost
Add the scenario material and machine costs per attempt, then adjust for the same expected failure rate.
scenarioExpectedCost = (((filamentWeight / 1000) * scenarioFilamentPrice) + (scenarioPrintHours * scenarioMachineRate)) / (1 - failureRate / 100)
Compare the two estimates
A negative result means the scenario is estimated to cost less per successful print; a positive result means it costs more.
costChange = scenarioExpectedCost - baselineExpectedCost
Example: 20% faster printing with a 10% filament price increase
Baseline material cost
(150 / 1000) × 25
$3.75
Baseline machine cost
8 × 1.50
$12.00
Baseline expected cost
(3.75 + 12.00) / (1 - 0.10)
$17.50
Scenario filament price
25 × 1.10
$27.50 per kg
Scenario print time
8 / 1.20
6.67 hours
Scenario expected cost
((0.15 × 27.50) + (6.67 × 1.50)) / 0.90
$15.69
Cost difference
15.69 - 17.50
-$1.81 per successful print
Final Result
The scenario expected cost is approximately $15.69 per successful print, about $1.81 lower than the $17.50 baseline estimate. Estimated print time falls by about 1.33 hours per print.
Assumptions
- ✓Every failed attempt uses the same material and machine time as a typical successful attempt.
- ✓The failure rate remains unchanged between the baseline and scenario.
- ✓An effective speed change affects print time inversely and does not model all slicer or machine constraints.
- ✓The machine hourly rate already includes whichever operating costs the user wants to track.
- ✓Material weight is assumed to remain the same when print speed changes.
Limitations
- !Actual failed prints may stop early and use less material and time than a full completed print.
- !Higher speed can change part quality, cooling behavior, support performance, and the real failure rate.
- !Slicer estimates may differ from actual run time because of acceleration, travel moves, pauses, and minimum layer times.
- !The model does not separately add setup, cleanup, post-processing, shipping, taxes, or inventory waste.
- !Material prices and machine rates can vary across suppliers, locations, and operating conditions.
Common Mistakes to Avoid
Entering the total material used across several prints instead of the weight for one completed print.
Treating a 20% speed increase as a 20% reduction in time; the model uses time divided by 1.20.
Using a failure rate as a decimal such as 0.10 when the input expects 10%.
Leaving the failure rate unchanged after making a speed change that is likely to affect reliability.
Comparing scenarios with different machine-cost inclusions, such as including labor in one rate but not the other.
Related Formulas
Frequently Asked Questions
How is the expected cost per successful 3D print calculated?
The calculator adds material and machine cost for one attempt, then divides by the success rate. A 10% failure rate means a 90% expected success rate, so attempt cost is divided by 0.90.
Why does a higher print speed reduce time by division instead of subtraction?
Speed and time are inverse. At 20% faster effective speed, the time estimate is the original time divided by 1.20, not reduced by exactly 20%.
Does the sensitivity formula change the print failure rate automatically?
No. The same failure-rate input is used for both estimates. Adjust it manually if the scenario is expected to change reliability.
Can the formula be used for resin printing?
Yes. Use the estimated resin weight, price per kilogram, machine duration, and hourly operating rate for the resin process.
What happens if the failure rate is zero?
Expected cost equals the cost of one attempt because no repeat attempts are assumed.
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