Human Years to Dog Years
Everyone converts their dog's age into human years. Flip the question and ask how old you would be as a dog or cat, and the math gets stranger than you might expect.
Converting human years to dog years is the reverse of the usual game. Instead of aging your dog up into human terms, you scale your own age down into a dog's or a cat's. It is good fun, and it is also a neat way to see how differently pets move through life. There is a catch, though: run the real formula backwards and the answers come out lopsided, for a reason worth understanding.
Below you get both common methods reversed, a size chart read backwards and the 2020 UCSD formula inverted, plus why the two disagree and why neither is something to take too seriously. For the normal direction, our dog years to human years page has the full chart.
The reverse question, and why it is backwards
The honest dog-to-human formula from 2020 is logarithmic: human age equals 16 times the natural log of the dog's age, plus 31. That shape captures how a dog crams a huge amount of aging into its first year, then slows down. When you invert it to go the other way, the logarithm turns into an exponential, and that is where the reverse gets weird.
Two things fall out. First, the formula has no answer below 31 human years, because a dog younger than one does not fit the model. Second, human adult years compress hard. By the formula a 40-year-old is under 2 dog years, a 60-year-old about 6, and an 80-year-old past 20, sailing beyond what most dogs ever reach. The same span that feels enormous to a person barely moves the dog-age needle in the middle, then rockets up at the end. That is expected, and it is what running a fast-early, slow-late curve in reverse looks like.
The old multiply-by-seven rule fails here just as it does forward. Flip it and you would divide your age by seven, which puts a 40-year-old at about 5.7 dog years. That happens to land near the chart answer, but the match is a coincidence. The seven-year rule assumes aging runs in a straight line, which it does not, so it drifts badly at both the young and the old ends.
The curve has been known for a long time. A French veterinarian, A. Lebeau, laid it out in 1953, lining up shared milestones like puberty and old age to show that dogs age roughly 15 to 20 times faster than people in the first year, then slow to roughly four to five human years for every dog year after that. Purdue researchers built on his work in 1997. Lebeau's point, seventy years old now, is the same reason the reverse never reduces to one tidy multiplier.
Human years to dog years, by size
Here is your age read backwards off the size charts, one column per dog size, with the UCSD formula alongside. Size matters as much in reverse as it does forward: because a giant breed ages faster, the same human age maps to fewer giant-dog years than small-dog years.
| Your age | Small | Medium | Large | Giant | UCSD formula |
|---|---|---|---|---|---|
| 20 | 1.6 | 1.6 | 1.6 | 1.8 | n/a |
| 30 | 3.5 | 3.5 | 3.5 | 2.9 | n/a |
| 40 | 6 | 5.7 | 5.4 | 4.3 | 1.8 |
| 50 | 8.5 | 7.8 | 7 | 6.1 | 3.3 |
| 60 | 11 | 10 | 8.8 | 7.5 | 6.1 |
| 70 | 13.5 | 12.2 | 10.7 | 8.9 | 11.4 |
| 80 | 16 | 14.4 | 12.6 | 10.1 | 21.4 |
Dog years by size, reverse of the PetToolkit age charts, with the 2020 UCSD formula. UCSD is n/a below 31, its model floor.
Two things stand out. Across a row, a giant dog reads years younger than a small one at the same human age, a 60-year-old is about 7.5 giant-dog years but roughly 11 small-dog years, the exact size gap that makes big dogs seniors so early. Down the UCSD column, the formula stays low in the middle then overshoots hard by 80, sailing past a real dog's lifespan. When a reverse calculator hands you one confident number, this whole spread is what it is quietly papering over.
Want to do it by hand with the formula? Take your age, subtract 31, divide by 16, then raise e, about 2.72, to that power. For a 55-year-old: 55 minus 31 is 24, divided by 16 is 1.5, and e to the 1.5 is roughly 4.5 dog years. Any calculator with an e-to-the-x button handles the last step.
Convert your age to cat years
Cats work the same way, read backwards off a cat chart. A cat reaches roughly 24 human-year equivalents by age 2, so scaling down, a person in their forties lands in the single digits of cat years and a person in their sixties around eleven. Cat aging does not shift with body size the way a dog's does, so one chart fits nearly every cat. The reverse numbers also climb more steadily than a dog's, without the exponential blow-up, because a cat chart is a gentler curve to run backwards in the first place.
| Your age | Cat years (chart) |
|---|---|
| 20 | 1.6 |
| 30 | 3.5 |
| 40 | 6 |
| 50 | 8.5 |
| 60 | 11 |
| 70 | 13.5 |
| 80 | 16 |
Reverse of the PetToolkit cat age chart.
Why it is only an estimate
Three caveats keep this honest, and none of them is small.
- Breed. The UCSD formula was fit to 104 Labrador Retrievers, so it speaks Labrador. UK VetCompass life tables put breed lifespans anywhere from about 4 years for a French Bulldog to nearly 13 for a Jack Russell, and each of those ages on its own clock.
- Size. Size alone can move a dog's real human-year age by years at the same birthday, which a single reverse figure cannot show.
- Method. Reading a lifespan chart backwards is a convention, since those charts were built to age pets up, and running them the other way was never their purpose.
So treat the reverse as a fun mirror, best kept clear of anything medical.
There is a nice twist in it, though. Because dogs front-load their aging, a 40-year-old owner is younger in dog years, under 2, than their 2-year-old dog is in human years, about 24. You are both middle-aged in your own species and worlds apart in each other's.
Want to try your own number? The dog age calculator has a reverse mode: switch it to human-to-pet, enter your age, and it estimates your age in dog or cat years. For the usual direction, see dog years to human years.
Frequently Asked Questions
How old would I be in dog years?
Read a dog-age chart backwards. On a medium-dog chart a 40-year-old maps to roughly 5 to 6 dog years and a 60-year-old to about 10. The 2020 UCSD formula gives smaller numbers, near 2 dog years at 40 and 6 at 60, because it is built on biology rather than a lifespan ratio. Both are rough.
What is the formula for human years to dog years?
Invert the UCSD dog-to-human formula. The forward version is human age = 16 times the natural log of dog age, plus 31. Solved for dog age it becomes dog age = e raised to the power of (human age minus 31) divided by 16. It only returns a sensible answer at 31 human years and up.
Why does the reverse give such strange numbers?
Because the forward formula is logarithmic. Dogs pack a lot of aging into their first year, so a wide band of human adult years squeezes into a narrow band of dog years, then shoots up at the top. A 40-year-old is under 2 dog years by the formula, while an 80-year-old lands past 20, beyond most dogs lifespans.
Is the human-to-dog conversion accurate?
Treat it as a party trick, not a health measure. The formula came from Labrador Retrievers, breed and size shift real aging, and reading a lifespan chart backwards is a convention rather than a biological fact. For anything that matters, use the normal dog-to-human direction and your vet.
How do I convert my age to cat years?
Use a cat chart in reverse. Cats reach about 24 human-year equivalents by age 2, so a 40-year-old person maps to roughly 6 cat years and a 60-year-old to about 11. Cat aging does not shift with size the way dogs do, so one chart covers most cats.