Debt snowball vs debt avalanche: the honest maths

The argument goes like this. The avalanche pays the highest interest rate first and is mathematically optimal. The snowball pays the smallest balance first and is psychologically optimal. Then someone says "personal finance is 80% behaviour" and the conversation ends without anyone having calculated anything.

Let us actually calculate it, because the size of the difference turns out to matter more than which side you are on — and in a lot of real cases the difference is much smaller than the argument suggests.

The rules, precisely

Both methods do the same two things:

1. Pay the minimum on every debt, every month.
2. Put every spare dollar on one target debt until it is gone, then roll that debt's minimum plus your extra onto the next target.

The only difference is how you sort the queue:

• Snowball — smallest balance first, ignoring interest rate.
• Avalanche — highest APR first, ignoring balance.

Everything else about them is identical, including the rollover, which is where most of the speed comes from in both.

The example

A real-shaped set of debts: $17,000 total, four accounts, and $600 a month available.

Debt	Balance	APR	Minimum
Medical bill (payment plan)	$900	0%	$45
Store card	$2,100	26.9%	$63
Credit card	$6,000	22.9%	$150
Car loan	$8,000	6.9%	$190
Total	$17,000		$448

Minimums come to $448, so there is $152 a month of extra payment to point at something.

The two queues are genuinely different:

• Snowball: medical ($900) → store card ($2,100) → credit card ($6,000) → car loan ($8,000)
• Avalanche: store card (26.9%) → credit card (22.9%) → car loan (6.9%) → medical (0%)

Note what the avalanche does with the medical bill: nothing. At 0% there is no reason to hurry, so it just runs at its $45 minimum and clears itself in month 20.

The results

Interest charged monthly on the outstanding balance, minimums held constant, no new borrowing.

	Snowball	Avalanche
Debt-free in	35 months	35 months
Total interest	$3,841	$3,610
Total paid	$20,841	$20,610
First debt cleared	month 5	month 12
Second debt cleared	month 14	month 20
Third debt cleared	month 29	month 29

The avalanche saves $232 over just under three years. That is about $6.60 a month. Both finish in the same month.

And the snowball clears its first debt seven months sooner, and its second debt six months sooner.

That is the honest answer for this household, and it is not the answer either camp usually gives. The avalanche wins, by an amount that would not cover a single car service.

Where the interest actually goes, in case the total hides something:

Debt	Interest, snowball	Interest, avalanche
Medical bill	$0	$0
Store card	$437	$297
Credit card	$2,359	$2,275
Car loan	$1,046	$1,038
Total	$3,841	$3,610

Almost the entire gap is the store card — $140 of it — because the avalanche attacks a 26.9% balance eight months earlier. Everything else is noise.

For scale: what minimums alone would do

Same debts, same interest, but $448 a month with no extra and no rollover:

77 months and $8,430 of interest.

So the extra $152 a month is worth 42 months and roughly $4,600. The choice of method is worth $232. The two decisions are not remotely the same size, and the extra payment is the one that is usually treated as an afterthought.

When the gap does get big

The $232 above is not universal. The gap between the methods widens with two things: how large the low-rate debt the snowball attacks first is, and how wide the spread of APRs is.

Here is the same $17,000 and the same $600 a month, arranged badly for the snowball:

Debt	Balance	APR	Minimum
Car loan	$1,500	2.9%	$60
Medical payment plan	$2,500	0%	$90
Credit card A	$6,000	27.9%	$150
Credit card B	$7,000	25.9%	$175

	Snowball	Avalanche
Debt-free in	43 months	41 months
Total interest	$8,533	$7,520
First debt cleared	month 9	month 26

Now the avalanche saves $1,013 and two months, because the snowball spends its first fifteen months clearing $4,000 of debt that costs almost nothing while $13,000 at 26-28% sits there compounding.

The rule of thumb this produces:

If your smallest debts are also cheap, and your expensive debts are large, the avalanche is worth real money. If your smallest debts are also the expensive ones, the two methods nearly converge — and if they nearly converge, take the momentum.

Run your own numbers before choosing. The gap is the deciding fact, and it is different for everyone.

What the research actually says about motivation

The psychological case for the snowball is not folklore, but it is narrower than it is usually stated.

Gal and McShane (2012), in the Journal of Marketing Research, studied real consumers in a debt settlement programme. What predicted whether someone eventually eliminated their debt was not how much of the total balance they had repaid, but what fraction of their individual accounts they had closed. Closing accounts — small victories — tracked with going the distance.

Kettle, Trudel, Blanchard and Häubl (2016), in the Journal of Consumer Research, took it further and tested the mechanism. Across several studies, including one with real cardholders, they found that concentrating repayment on a single account rather than spreading it across accounts increased motivation to get out of debt — and that the driver was perceived progress, not the amount repaid. Spreading the same money thinly across five accounts produced no visible movement anywhere, and people disengaged.

Two things follow, and only two:

1. Concentration matters. Do not split your extra payment across debts. Both the snowball and the avalanche already do this correctly; a "little bit extra on everything" strategy is the one the research argues against.
2. Visible completion matters. A debt that disappears is worth more motivationally than a balance that shrinks. That is a real argument for the snowball where the gap is small.

What this research does not say is that the snowball beats the avalanche in total money, or that it works for everyone. Neither study set out to test that, and neither found it.

Who should choose which

Choose the avalanche if:

• You have run both and the gap is meaningful to you — more than a couple of hundred dollars, or more than a month
• Your smallest balance is large and cheap (a low-rate car loan, a 0% payment plan) and your expensive debt is big
• You have finished a multi-year financial plan before
• You find "this is the optimal answer" motivating in itself, which some people genuinely do

Choose the snowball if:

• You have two or three small balances that would clear inside six months
• You have started and abandoned a payoff plan before
• The gap in your numbers is small — and, as shown above, it often is
• More than about four open accounts are making the situation feel unmanageable

A defensible hybrid: clear anything you could pay off within roughly two months first, whatever its rate, then switch to strict avalanche for everything that is left. You buy the early wins cheaply and pay optimal rates for the long middle. In the first example above, that hybrid clears the $900 medical bill and then behaves like the avalanche.

Five things that override both methods

1. An employer pension or 401(k) match. Free 50-100% on your contribution beats any consumer APR. Take the match first unless a debt is in default.
2. A 0% promotional rate that is about to end. Clear it before it reverts, whatever the queue says.
3. Debt in collections, arrears, or anything with legal consequences — council tax, child support, tax debt, secured debt where default means losing the car. Handle these first, and get free regulated debt advice rather than budgeting your way through them alone.
4. A debt owed to a person. The interest rate is 0% and the real cost is the relationship. Rank it wherever you need to.
5. Not having any buffer at all. A payoff plan with $0 set aside means the next flat tyre goes on the credit card, and you undo four months of work. A small starter fund of a few hundred dollars first is not a delay, it is what stops the plan reversing.

Compute it yourself

Payoff months for a single debt: NPER

For one debt at a fixed payment, the number of months is a closed-form calculation. In Excel or Google Sheets:

=NPER(rate/12, -payment, balance)

For the $6,000 credit card at 22.9% paying $250 a month:

=NPER(0.229/12, -250, 6000)   →  32.4 months

The payment goes in negative because NPER follows the cash-flow sign convention: money leaving you is negative, the balance you hold is positive. Get the sign wrong and you get an error or a nonsense result.

The algebra behind it, if you would rather see it:

n = -ln(1 - (r × B) / P) / ln(1 + r)

  r = monthly rate (APR ÷ 12)
  B = balance
  P = monthly payment

The failure case is the interesting one. If P ≤ r × B, the payment does not even cover the interest, the logarithm takes a negative argument, and the formula fails — correctly, because the debt never gets paid off. The store card in the first example is close to this: $2,100 at 26.9% accrues $47.08 in the first month against a $63 minimum, so $15.92 goes to principal. NPER says 62 months at that rate. Minimum payments are engineered to sit just above this line.

Two more useful ones:

Total interest on one debt    =NPER(...) * payment - balance
Payment needed for a deadline =PMT(rate/12, months, -balance)

Why NPER is not enough for a plan

NPER handles one debt at a fixed payment. It cannot model the rollover, and the rollover is the whole point — when your $900 medical bill clears in month 5, its $45 joins your $152 extra, and the next target starts receiving $197.

To model that you need a month-by-month schedule: one row per month, one column per debt, and for each cell — add interest, subtract the minimum, then subtract any extra according to the queue, then carry the balance forward. It is about forty rows of arithmetic per year and it is genuinely fiddly to get right, mostly because of the edge cases (the month a debt is overpaid, the month the extra has to split across two debts).

Our Debt Payoff Planner Spreadsheet is that schedule for up to fifteen debts over ten years, with a dropdown that recalculates the whole thing as snowball, avalanche or your own order, so you can see your own version of the table at the top of this post in about two minutes. If you would rather build it yourself, the paragraph above is the algorithm — there is nothing hidden in it.

The part that matters most

Across every scenario on this page, changing method moved the finish line by 0 to 2 months. Adding $100 a month to the payment moved it by six months and saved about $836 in interest — more than three times what the method choice was worth.

So: pick the queue you will stick to, concentrate your extra payment on one debt at a time, and then spend your remaining energy on making the extra payment bigger. That last part is the lever. The snowball-versus-avalanche argument is, for most people, a rounding error with a fan club.

If you want to work it out on paper, there are free printable sample pages to start from, and the 50/30/20 calculator will tell you roughly how much extra your income should be able to support.