Daily Reducing Balance Calculator
A balance that shrinks by a percentage each day does not shrink in a straight line. It falls fast at first, then slower, because each day the percentage is taken from a smaller amount. This daily reducing balance calculator gives you the exact amount left after a set number of days at a set daily reduction rate, with the day-by-day path shown so you can see the curve for yourself.
The daily number here is a percentage reduction applied to whatever balance remains that morning. This tool does not add loan interest, take payments, or convert an annual rate. It answers one question cleanly: if an amount falls by the same percentage every day, what is left after a given number of days?
How it was calculated
This is a pure percentage-decay model. It does not add interest, subtract fixed payments, or follow a tax depreciation schedule, so do not use it as a loan amortization or a MACRS calculation.
Quick Answer
- Quick Answer
- How to use the daily reducing balance calculator
- The reducing balance formula, step by step
- Worked example: 1,000 at 2% per day for 10 days
- Reducing balance or straight-line reduction: which model fits?
- What competing reducing balance calculators miss
- Where a daily percentage reduction actually shows up
- Frequently Asked Questions
- Add This Calculator to Your Website
- References
How to use the daily reducing balance calculator
Enter the starting amount, the daily percentage reduction, and the number of whole days. Press Calculate and the result shows the final balance with the working underneath it, so you can check the formula instead of trusting a single number.
Start with the balance you have. That is the initial amount, in dollars, units, or any other measure, as long as you stay consistent.
Set the daily rate as a percentage of what remains. A 2% daily reduction means you keep 98% each day. It does not mean you lose 2% of the original amount each day.
Count whole consecutive days. Weekends and holidays count unless you subtract them yourself. If your process only runs on business days, enter the business-day count.
Read the final balance, then check the path. The table below shows every day of the worked example. If your real balance follows a different path, your rate is not constant, and a single-rate model will drift.
If your balance is growing by a percentage each day instead, that is the mirror problem. The daily increment calculator handles daily growth, and the daily compound calculator handles compound growth over a period. This page is only for the shrinking case.
The reducing balance formula, step by step
The formula is exponential decay with a daily step: multiply the starting amount by the keep factor once for each day.
This is the discrete form of the exponential decay model taught in algebra and calculus, where a quantity loses a fixed proportion of itself in each period. Khan Academy presents the same structure for decay problems, and college algebra texts use it for half-life: the time for the balance to halve depends only on the rate, not on the starting amount. At 2% per day, for example, any balance halves in about 34 days, whether it starts at 1,000 or at 1,000,000.
Contrast that with a straight-line reduction, where the same dollar amount comes off every day. Straight-line reaches zero on a predictable date. A reducing balance never quite reaches zero in the math: it gets closer and closer, which matches things like a depreciating asset value or a slowly consumed stockpile better than it matches a loan being paid off in fixed installments.
Worked example: 1,000 at 2% per day for 10 days
The calculator is pre-filled with this case, and the table is the exact path its formula produces, rounded to two decimals each day.
| Day | Balance at start of day | Reduction that day (2%) | Balance at end of day |
|---|---|---|---|
| 1 | 1,000.00 | 20.00 | 980.00 |
| 2 | 980.00 | 19.60 | 960.40 |
| 3 | 960.40 | 19.21 | 941.19 |
| 4 | 941.19 | 18.82 | 922.37 |
| 5 | 922.37 | 18.45 | 903.92 |
| 6 | 903.92 | 18.08 | 885.84 |
| 7 | 885.84 | 17.72 | 868.13 |
| 8 | 868.13 | 17.36 | 850.76 |
| 9 | 850.76 | 17.02 | 833.75 |
| 10 | 833.75 | 16.67 | 817.07 |
Two checks confirm the table. First, the direct formula: 1,000 x 0.98^10 = 817.07, the same final balance the calculator returns. Second, the daily reductions add up: they total 182.93, and 1,000 minus 182.93 is 817.07. If a hand calculation of yours gives 800, you subtracted 2% of the original 1,000 ten times, which is the straight-line answer, not the reducing balance answer.
Reducing balance or straight-line reduction: which model fits?
Pick the model that matches how the loss actually happens, not the one that is easier to compute.
Daily reducing balance (percentage)
- Same percentage off a shrinking balance each day
- Large reductions early, smaller reductions later
- Never quite reaches zero
- Fits: percentage depreciation, proportional consumption, decay processes
Straight-line reduction (fixed amount)
- Same dollar or unit amount off every day
- Predictable date when the balance hits zero
- Simpler to budget and audit
- Fits: fixed daily usage, fixed installments, daily straight-line depreciation schedules
Tax depreciation adds rules on top of either model. Under IRS Publication 946, MACRS declining balance uses a set rate on the adjusted basis and switches to straight-line when that gives an equal or larger deduction, with conventions for the first and last year. This calculator does none of that switching or convention work. Use it to understand the shape of a reducing balance, then use proper depreciation guidance for a tax figure. Finance teams modeling a balance that also earns or is charged interest need a different tool as well, since interest changes the balance in the opposite direction while payments change it in steps. The decreasing interest calculator covers the related case where the interest itself is falling.
What competing reducing balance calculators miss
The top results for this keyword split into two camps, and both leave something important unsaid.
Miss 1: loan language wrapped around decay math. Several competing pages describe daily reducing balance as a loan interest method, with annual rates divided by 365 and payments recalculating interest, then present a calculator that does something simpler. Borrowers who trust that framing will expect payment and interest behavior the math does not contain. This page states the limit up front: no payments, no interest accrual, no annual rate conversion. What you enter as a daily percentage is exactly what comes off each day.
Miss 2: a final number with no path. Most tools return only the end balance. Without the day-by-day path you cannot spot the most common input error, using a rate taken from the original amount, and you cannot compare the model with a real balance history. The worked example here shows all ten days, and the result box shows its working, so a mismatch is visible immediately.
Miss 3: silence about whole days and edge rates. Older help text for tools like this one has claimed fractional days work. In this calculator the day count is a whole number: enter 10.9 days and it calculates 10 days. Rates at or above 100% are also left unexplained elsewhere. At exactly 100% the balance is zero after day 1. Above 100% the formula produces values that do not describe a real balance, so do not use it there.
Where a daily percentage reduction actually shows up
Asset values under percentage depreciation are the textbook case: a vehicle or machine losing a set percentage of its current book value each period follows this curve, which is why declining balance depreciation exists as a method in the first place. Inventory and reserves consumed in proportion to stock, a stockpile drawn down by a percentage a day, follow it too, as do balances in simple decay models for budgeting how long a resource lasts.
The model fails where the daily loss is fixed in dollars, where deposits or payments interrupt the curve, or where the rate itself changes over time. In those cases split the period at each change and run the calculator once per segment, using the end balance of one segment as the start of the next. That segmented approach is exact for this formula and keeps every assumption visible.
Frequently Asked Questions
A daily reducing balance is an amount that falls by the same percentage each day, with the percentage always applied to the balance remaining that day. Because the balance shrinks, the dollar amount of each daily reduction shrinks too, so the balance curves downward instead of falling in a straight line.
Final balance = initial amount x (1 - daily reduction rate / 100) raised to the number of days. For 1,000 at 2% per day for 10 days: 1,000 x 0.98^10 = 817.07. The term in brackets is the keep factor, the share of the balance that survives each day.
No. This calculator counts whole days only, so a value like 10.9 days is treated as 10 days. Enter the whole-day count you want modeled. For a partial final day, calculate to the last whole day and then apply one partial-day adjustment by hand.
At 0% nothing is reduced, so the final balance equals the initial amount for any number of days. At 100% the whole balance is removed on day 1, so the final balance is 0.00. Rates above 100% do not describe a real balance and should not be used.
Not by itself. A reducing balance loan also charges interest on the outstanding balance and subtracts payments on set dates, so the balance moves for three reasons at once. This calculator models only one of them: a fixed daily percentage reduction, with no interest added and no payments taken off.
The final balance equals the initial amount. With no days elapsed, the keep factor is raised to the power of zero, which is 1, so nothing has been reduced yet.
No. It treats every day the same and assumes consecutive days. If your reduction only happens on business days, count only those days and enter that smaller number.
The formula would grow the balance with a negative rate, but that is not what this tool is for and the result is easy to misread. Use a daily growth or daily compound calculator for increasing balances, where the inputs and labels match the job.
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References
- Internal Revenue Service, "Publication 946: How To Depreciate Property", on the declining balance method, applying the same rate to the adjusted basis each year and switching to straight-line. IRS: Publication 946, How To Depreciate Property. Accessed October 2026.
- Khan Academy, "More exponential decay examples", presenting the decay formula as the starting amount times a decay factor raised to the time elapsed. Khan Academy: More Exponential Decay Examples. Accessed October 2026.
- Lumen Learning, "Exponential and Logarithmic Models", College Algebra, on half-life and exponential decay models. Lumen Learning: Exponential and Logarithmic Models. Accessed October 2026.
- Lumen Learning, "Exponential Growth and Decay", on half-life as the time for a decaying quantity to fall to half its original amount. Lumen Learning: Exponential Growth and Decay. Accessed October 2026.
- Microsoft, "150 percent reducing balance depreciation", Dynamics 365 Finance documentation, on reducing balance depreciation posting by period including daily posting. Microsoft: 150 Percent Reducing Balance Depreciation. Accessed October 2026.
- Washington State Department of Enterprise Services, "Depreciation: Daily Straight Line", the fixed-amount daily alternative used as the contrast model. Washington DES: Daily Straight-Line Depreciation. Accessed October 2026.
- Pearson, "Half-Life Calculator" background, on first-order decay following N = N0 e to the power of minus kt and fraction remaining. Pearson: Half-Life and Exponential Decay Background. Accessed October 2026.
- LegalClarity, "What Is a Declining Balance? Depreciation Explained", on applying a fixed rate to a shrinking book value under the declining balance method. LegalClarity: Declining Balance Depreciation Explained. Accessed October 2026.