The Scientific Formula for Dog Age (With Examples)

October 7, 2026

By PrimeFreeTools Editorial Team, written from hands-on use of our own tools.

Dog Age & Care

Human-equivalent age = 16 × ln(dog age in years) + 31. That is the whole formula — natural logarithm, not base-10 — from Wang et al., UCSD 2020. Here it is worked through.

Worked examples

Age 1: ln(1) = 0 → 31
Age 2: ln(2) ≈ 0.693 → ≈ 42
Age 4: ln(4) ≈ 1.386 → ≈ 53
Age 7: ln(7) ≈ 1.946 → ≈ 62
Age 10: ln(10) ≈ 2.303 → ≈ 68
Age 13: ln(13) ≈ 2.565 → ≈ 72

Using it correctly

Use decimal ages (4 years 6 months = 4.5), never base-10 logs, and remember the Labrador calibration — adjust for size at the extremes. Or skip the arithmetic: the dog age calculator runs this plus breed correction instantly.

Questions & answers

Natural log or log10?

Natural log (ln). Base-10 gives wildly wrong answers — the classic implementation bug.

What about puppies under 1?

The formula gives sub-31 values that compress oddly; developmental milestones describe puppies better than any number.

Where was this published?

Cell Systems, 2020, Wang et al., UC San Diego. Search the title for the full methods.