How much biking is equivalent to 1 mile of jogging?

I can do a full out hour on the bike and burn ~1200 kcal.
I can do an hour of high pace running and burn ~ 1200 kcal.

On the bike I will have covered 3x the distance.

YMMV

I would say normally one has to ride a bike twice as long as they are running. (With a huge list of assumptions and caveats)

How do you know your calories burned?

Frankly 1200 in a hour seems high even if you are a large person. Yes you are specifying “full out” and “high pace” but those kept up for an hour are different intensities than for a sprint …

I don’t “know”.
I have a running watch with a heart monitor. It guesstimates my calories burned.

It is probably absolutely useless in absolute terms but it allows me to compare efforts in different sports.

Think you need a power meter to really know calorie expenditure for cycling - they’re pretty common now amongst amateur racers / enthusiasts, but you wouldn’t see one on a recreational bike.

Heart rate monitor with a gps is a bit of a stab in the dark ime - there probably is a steady sort of effort where they’re not too far off, but what that is IDK.

I’m increasingly suspicious that these guesstimates, even with power meters, but maybe less so factoring in heart rate zone you are in, are pretty poor.

As a case in point - when I was training for a half iron man I was in decent aerobic shape. My swim technique still was ugly. Fishtailing wouldn’t do the horribleness justice; I was wrestling the water and the water always won. I went swimming with my friend who had been a childhood swimmer. He swam at least 50% faster than I did but I am sure that per time unit I was burning 50% more calories!

Even cycling there are those who are relatively wasting energy by poorer form, energy that is not producing power, and those who are all efficiency.

Running too. I see good runners. They glide across the ground. And there are the likes of me that thud along the pavement. Same speed at same body weight is different fraction of HRmax and different calories burned. Gotta be.

It’s pretty accurate for cycling with a power meter - typically within 5%, because the work done is being measured accurately. The assumption is what percentage of food energy is converted to pedal energy, which is 20-25% and obv there will be some variability here.

As the conversion from KJ to Kcal is 4.2, it falls out that your KJ of work on the bike is close to your kcal expenditure.

You won’t get such a clear picture in swimming or running as you can’t directly measure power afaik. There are many surrogate approaches though as the commercial market would be massive - I believe the current technology for running is to use wearable accelerometers.

I think that the way it’s usually done in sports medicine is to measure the amount of air breathed by the athlete, and the amount of carbon dioxide exhaled. When you see someone running on a treadmill with plastic tubes on their face, that’s what it’s for.

Of course, this isn’t directly useful for hobbyists just out on a morning jog or whatever, but it can be used to calibrate models based on things that are easier to measure, like speed and pulse rate.

I was in a Corporate Athlete program (it’s a program for holistic “executive” wellness, not a program to train athletes)

There was a guy in the group who did half marathons, and was training for a full. When he and I were running at 9 mph (highest I could manage for more than a minute or two) the carbon dioxide I was producing was higher per kg than he was.

Even if you could measure power directly I don’t think it would work as well.

For cycling ultimately the vast majority of muscle use gets transferred to the pedals. Not all of course, muscles used and energy expended holding yourself supported in the drops position as a static hold for example, but most. Pulling on the bars as you get out of the saddle to climb transfers to pedals… so on.

Running less so. There is a lot more to said for “running efficiency”. Besides heat loss there is muscle use not producing the power of the activity. And in swimming??? Hoo boy. Rowing? Lots of difference based on technique and lots of movement not producing power (the whole catch).

Yes that is the gold standard. If there is an actual basis for the claim that a cycling power meter will calculate to within 5% it is based on comparison to that.