Diminishing Rate Calculator
A diminishing rate is a per unit price, charge or deduction that falls as quantity grows: the first units cost the most and later units get cheaper. This diminishing rate calculator models that fall five different ways, then reports the rate at your target quantity, the total cost, the savings against the starting rate, and how the total bends across five comparison quantities.
Modeling tool. Efficiency and strategy scores are simplified indicators for comparing scenarios, not financial advice.
Quick Answer
- Quick Answer
- The classic case: diminishing balance depreciation
- Worked example: $100 falling 10% every 100 units
- Five models, one set of inputs, five different answers
- Diminishing rate is not diminishing returns
- Reading every line of the result
- Two controls that did not change the math, removed
- What competing calculators miss
- Frequently Asked Questions
- Add This Calculator to Your Website
- References
The classic case: diminishing balance depreciation
The most searched use of a diminishing rate is asset depreciation, where each period deducts a fixed percentage of the shrinking book value instead of the original cost. A machine bought for $10,000 and depreciated at 20% per year shows the pattern in three lines: year 1 deducts $10,000 x 20% = $2,000 and leaves $8,000; year 2 deducts $8,000 x 20% = $1,600 and leaves $6,400; year 3 deducts $6,400 x 20% = $1,280 and leaves $5,120. The deductions themselves diminish, which is the whole point of the method.
This calculator generalizes that pattern from years to quantities. With the Stepped Geometric Reduction model, the tool applies a fixed percentage fall at each quantity interval, each time on the rate left after the previous fall, which is the declining balance shape with units in place of years. For the yearly deduction itself on a real asset, the depreciation expense calculator works period by period, and the diminishing value depreciation calculator follows the Australian tax formula with effective life and days held. Those two pages file the claim; this page models the curve.
Worked example: $100 falling 10% every 100 units
The calculator is pre-filled with this case, and every figure below is what it returns, including the five scenario totals it builds from the maximum quantity of 1,000.
| Measure | Result | How it is reached |
|---|---|---|
| Steps of decline | 4 | (500 - 1) / 100 = 4.99, rounded down to 4 whole intervals |
| Rate at target (500 units) | $65.61 | $100 x 0.94 |
| Total cost at target | $32,805.00 | $65.61 x 500 units |
| Cost at the initial rate | $50,000.00 | $100 x 500 units |
| Savings vs initial rate | $17,195.00 (34.4%) | $50,000.00 - $32,805.00 |
| Optimal quantity (Maximize Revenue) | 700 at $53.14 = $37,200.87 | 70% of the 1,000 maximum, rated with the same model |
| Efficiency rating | 5.5 / 10 | Blend of fall toward the floor and target vs optimal quantity |
| Scenario quantity | Rate there | Total cost |
|---|---|---|
| 200 units | $90.00 | $18,000.00 |
| 400 units | $72.90 | $29,160.00 |
| 600 units | $59.05 | $35,429.40 |
| 800 units | $47.83 | $38,263.75 |
| 1,000 units | $38.74 | $38,742.05 |
Read the totals column carefully, because it teaches the central lesson of diminishing rates: the per unit rate keeps falling, yet the total keeps rising. Cheaper units are not a cheaper bill when quantity grows faster than the rate falls. That is exactly the trade-off volume pricing, learning curves and depreciation schedules all have to manage.
Five models, one set of inputs, five different answers
The model menu is not five names for one formula. Run the same pre-filled inputs through each model and the rate at 500 units lands in five different places, because each curve falls in its own way.
| Model | Formula the tool applies | Rate at 500 | Total at 500 |
|---|---|---|---|
| Exponential Decay | Initial x decay(q - base) / half-life | $94.88 | $47,439.16 |
| Stepped Tiers | The tier rate for the quantity band | $80.00 | $40,000.00 |
| Stepped Geometric Reduction | Initial x (1 - d%)whole intervals | $65.61 | $32,805.00 |
| Power Law | Initial x (q / base)-d% | $53.72 | $26,857.96 |
| Logarithmic Decline | Initial - (initial - min) x ln(1 + (q - base) / interval) / ln(1 + steepness) | $10.00 | $5,000.00 |
Three honest warnings belong with that table. First, the model name matters: the Stepped Geometric Reduction rate does not slide down evenly and does not fall by the same dollar amount each time. It holds flat inside each 100 unit interval and drops by 10% of the rate remaining at each boundary, a stepped geometric fall. A true linear reduction would instead subtract the same slice of the original rate at every step, and no model on this page does that. Second, the Logarithmic result is the floor, not the curve: at steepness 1 the raw formula lands near negative $132 at 500 units, so the $10 floor takes over, and raising the steepness is what softens that model. Third, the Stepped Tiers row uses the pre-filled bands ($100 to 250 units, $90 to 500, $80 to 750, $70 above), so 500 units lands in Tier 3 at $80. Tier bands are the same published-discount structure the discount percent calculator handles one percentage at a time.
Diminishing rate is not diminishing returns
These two phrases sound like one topic and they are not, and the two calculators on this site are built differently because of it. A diminishing rate, this page, is about a per unit figure falling as quantity rises: prices, charges, deductions. Diminishing returns, the economics law, is about output: each extra unit of input producing less extra output than the one before, measured as marginal product. This tool never asks for output and never computes a marginal product. The diminishing returns calculator does exactly that, comparing input and output pairs and classifying each step as increasing, diminishing or negative returns. If your question has the words per unit, price or rate in it, stay here. If it has workers, fertilizer, ad spend and output in it, go there.
Reading every line of the result
The headline is the rate at your target quantity, and everything under it answers a follow-up question. Total cost at target multiplies that rate by the target quantity. Savings and the discount percentage compare that total against holding the initial rate for all units. The scenarios block prices five quantities up to your maximum with the same model, so you can watch the curve bend instead of guessing it from one point.
The optimal quantity line is a rule of thumb, not a solver: Maximize Revenue reads 70% of your maximum, Maximize Profit 50%, Market Penetration 80%, and Maximize Volume and Customer Retention both read the full maximum, 100%: the retention goal is set at the full maximum by design, which the goal menu label itself now states. The efficiency rating, from 1 to 10, blends how far the rate has fallen toward your floor with how close the target sits to that optimal quantity, which is why the worked example scores 5.5: a solid fall, at a target below the revenue optimum. The break-even quantity only appears when you enter a break-even target, and it is that target divided by the floor rate, rounded up: a $10,000 target at a $10 floor needs 1,000 units. One display quirk worth knowing: the formula line under the results always quotes your diminishing rate and interval, even for the Exponential and Power Law models, which do not use those two fields.
Two controls that did not change the math, removed
The levers that are real: the model menu, the initial rate, the floor, the base and target quantities, and the one or two fields your chosen model actually reads. Stepped Geometric Reduction reads the diminishing rate and interval. Exponential Decay reads the decay factor and half-life. Logarithmic Decline reads the interval and steepness. Power Law reads the base quantity and diminishing rate. Stepped Tiers reads the tier table and nothing else. Changing a field your model does not read will not move the result, and the tooltips on each field say which model uses it.
What competing calculators miss
Search this term and the ranking pages are almost all single-formula depreciation tools: cost, salvage, life, one declining balance schedule. That answers the tax-flavored question well, and Microsoft documents the same fixed-declining balance method for the Excel DB function, so the formula itself is not in dispute. What those pages cannot do is everything else a diminishing rate gets used for.
Miss 1: one curve only. A volume discount, a learning curve and a depreciation schedule do not fall the same way, and a tool with one curve forces your problem into its shape. The learning curve literature going back to Wright's 1936 airplane cost study is a power law, not a declining balance, and this page models it as one. Five curves with a floor is the difference between a depreciation gadget and a rate modeler.
Miss 2: no tiers. Real discount schedules are published as bands, and single-formula tools have nowhere to put them. The stepped tiers model here takes four thresholds with their rates and reports your current tier and the distance to the next one.
Miss 3: no comparison. One answer at one quantity hides the trade-off the worked example table shows: totals rising while rates fall. The five scenario totals make that visible at a glance.
One honest limit in the other direction: this is a modeling tool, not a tax depreciation schedule. It has no effective life tables, no days-held proration and no jurisdiction rules, so do not file a return from it. For an actual claim, use the dedicated depreciation pages linked above and confirm the treatment with a qualified accountant.
Disclaimer: this calculator is an educational modeling tool. Efficiency and strategy scores are simplified indicators for comparing scenarios. It is not financial or tax advice.
Frequently Asked Questions
It depends on the model. The classic declining balance form is final value = initial x (1 - rate/100) to the power of the periods, so $1,000 falling 10% per period for 3 periods is $1,000 x 0.9 x 0.9 x 0.9 = $729. This calculator applies five versions of that idea across quantity instead of time, and every version stops at the minimum rate floor you set.
It is depreciation charged as a fixed percentage of the current book value, so the deductions shrink every period. A $10,000 asset at 20% deducts $2,000 in year 1 leaving $8,000, then $1,600 leaving $6,400, then $1,280 leaving $5,120. The Stepped Geometric Reduction model on this page follows the same shape across quantities instead of years.
A diminishing rate is a per unit price, charge or deduction that falls as quantity grows, which is what this calculator models. Diminishing returns is the economics law that each extra unit of input produces less extra output than the one before. This tool never uses output figures; the diminishing returns calculator on this site does, and classifies each input step for you.
Stepped Geometric Reduction for predictable percentage steps at fixed intervals, such as depreciation-style schedules. Exponential Decay for smooth falls that flatten out, Stepped Tiers for published volume discount bands, Power Law for learning curve effects, and Logarithmic Decline when the fall should be strong early and then ease off. The comparison table above shows how far apart the five answers can sit on identical inputs.
Because at steepness 1 the logarithmic fall is very sharp. On the pre-filled inputs the raw formula lands near negative $132 at 500 units, so the $10 minimum floor takes over and the tool reports $10.00. Raise the steepness value to soften the curve, or raise the floor if the rate should stop higher.
It is a 1 to 10 indicator that blends two things: how far the rate at your target has fallen from the initial rate toward your floor, and how close your target quantity is to the suggested optimal quantity for your goal. The worked example scores 5.5 out of 10. Treat it as a comparison score between scenarios, not as a grade of the decision itself.
Enter up to four quantity thresholds with the rate that applies from each one. Any quantity uses the rate of the highest threshold it has reached, so with the pre-filled bands a target of 500 units sits in Tier 3 at $80, with the next tier 250 units away at $70. The result also names your current tier whenever this model is selected.
It is your break-even target divided by the minimum rate floor, rounded up: how many units sold at the floor rate would cover the target. A $10,000 target at a $10 floor gives 1,000 units. Leave the break-even target at 0 and the line shows as not applicable.
Because this tool defines both goals as the full maximum quantity. The goal menu sets the suggested optimal quantity as a share of your maximum: Maximize Revenue 70%, Maximize Profit 50%, Market Penetration 80%, and Maximize Volume and Customer Retention both 100%. Pick either of those two and the suggested quantity, the rate there and the total are the same, and the retention option is labelled with that fact in the menu itself.
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References
- Internal Revenue Service, "Publication 946: How To Depreciate Property" - the federal reference for depreciation methods, including declining balance, MACRS and salvage value treatment. IRS: Publication 946, How To Depreciate Property. Accessed October 2026.
- Internal Revenue Service, "A Brief Overview of Depreciation" - the IRS summary of what depreciation is, what property qualifies, and when the deduction begins. IRS: A Brief Overview of Depreciation. Accessed October 2026.
- Microsoft Support, "DB function" - the fixed-declining balance depreciation formula as implemented in Excel, rate = 1 - (salvage / cost) to the power of (1 / life). Microsoft Support: DB Function. Accessed October 2026.
- Microsoft Support, "DDB function" - the double-declining balance method and its formula, the accelerated cousin of the curves modeled on this page. Microsoft Support: DDB Function. Accessed October 2026.
- Wikipedia, "Learning curve" - the power law relationship between cumulative quantity and unit cost first quantified by T. P. Wright in 1936, behind the Power Law model. Wikipedia: Learning Curve. Accessed October 2026.