Debt Dynamics Calculator

See how interest, growth and new borrowing combine to move the US debt ratio over 30 years. The starting values are the rough numbers of the current US economy (october 2026). It is a teaching model, not a forecast.

next debt ratio = debt ratio × (1 + r) ÷ (1 + g) + p

Rising

Debt in year 30

Deficit today

Holds debt flat at

Long-run level

Debt as % of GDP, next 30 years

Debt ratio Starting level

Year

Debt

Interest rate

of which sentiment

Total deficit

Where the change in year 1 comes from

Snowball on existing debt, (r − g) applied to the debt

New primary deficit

Net change, in points of GDP

How the model works

b is federal debt divided by GDP. p is the primary deficit, the deficit before interest, as a share of GDP. r is the average interest rate on all outstanding debt. g is nominal GDP growth, which is real growth plus inflation.
Each year the debt grows by its interest and by the new borrowing, while GDP grows by g. Dividing the two gives the formula at the top.
The interest rate moves in a straight line from today's value to the year-10 value and then stays there. This stands in for old low-rate debt being refinanced at market rates.
Total deficit is the primary deficit plus interest on the opening debt, as a share of GDP.
If r is below g, the ratio levels off at p ÷ (1 − (1 + r) ÷ (1 + g)), however large that is. If r is above g, there is no level-off, and only a primary surplus can stop the climb.
Market sentiment works as a risk premium. Above the comfort level, investors ask for extra yield on new debt in proportion to how far the debt ratio is above it. Because only part of the debt is refinanced each year, the premium reaches the average rate gradually, with an average maturity of 6 years. Nothing jumps.
Published estimates of this effect are often a few basis points of extra yield per point of debt-to-GDP, so 20 to 30 basis points per 10 points is a plausible range. Treat the slider as a rough dial. A basis point is one hundredth of a percentage point.
The model keeps g and p fixed. In reality they respond to policy and to the economy. For official projections, see the Congressional Budget Office.