# Is there a standard equivalent for effort between distance and elevation?

I'm starting to keep track of how far I ride on paper and while it's nice to have the data, I'd like to know how different rides stack up.

I have one path I like to take which is really flat and goes about 30 miles out (I usually only do 10 and then turn around), but I've found this ride is much easier for me than the other route I take which nets me about 12 miles and about 500 feet in elevation.

I saw on another SE that they calculate 500 feet elevation gain into one mile, but this doesn't seem that accurate for a bike.

So, what I want to know is if there is a standard calculation for "effort" or distance between distance and elevation gain, given perhaps average speed or any other relevant factors.

• No, given that you're using different muscle groups and what not. Jul 2, 2015 at 20:12
• @Ross has mentioned speed, and that's my question. How fast are you doing these rides? Jul 3, 2015 at 0:49
• @andy256 The flat sessions, 15 MPH on a good day and the hills about 13 MPH average Jul 3, 2015 at 1:21
• And what is the total amount of climbing? 500 ft (160m) of climbing in 12 mi (19 km) is less than 1% average - that's flat in my book. But you mention hills plural, meaning there's up and down, so I take the 160m as net altitude gain. What's the total gain? And how steep? Jul 3, 2015 at 1:45
• I also apologize if imperial measurements are not the norm on this SE. Should I just switch to metric for the sake of consistency on the SE or doesnt it matter? Jul 3, 2015 at 19:33

If you really want to measure how much effort you're putting in, you should look into getting a power meter. It measures the actual wattage you output, and can therefore be used to calculate total energy output. However, they are quite expensive.

The other option is to get a heart rate monitor along with cadence and speed meters which together can give you a reasonable estimate of how much energy you used. This ends up being much cheaper than a power meter, but is less accurate.

These are the preferred methods if you a really want to track how hard you are training. This is because many things can effect how much effort it takes to cycle such as hills (like you mentioned), but also wind, your body position, and the road surface itself.

• While a lot of people knock heart rate monitors as "less accurate", they trade that accuracy for ease of setup (no need for a new rear wheel) and expense. They are also useful for other endeavors besides cycling as well. They are an excellent choice for more recreational cyclists. Jul 2, 2015 at 20:29
• Cycleops has a heart rate power meter that does a bunch of number crunching (I suspect some sort of statistical time series model) that gives decent average power over longer time periods (I.e., > 30 sec). It won't give an accurate peak power estimate and is affected by condition (e.g., fatigue, hydration levels affect HR), but as an inexpensive means of getting a ball park estimate of average power it is surprisingly good. Ran it beside a regular power meter and it was pleasantly surprised. Of course this needs an Ant+ bike computer (\$\$) to read it. Jul 2, 2015 at 21:12
• A third option is to track "session RPE" using the 10-point (or 20-point) Borg scale, which doesn't require any hardware investment at all -- and, once you know how to use it and get some experience, is roughly about as accurate as looking at average heart rate. Jul 2, 2015 at 22:46
• @Rider_X Some phones have Ant+ built in, so you may be able to get by with that. Also, there are some alternatives to "bike computers". I have an Garmin Oregon 450 (discontinued), which is very similar to the Garmin Dakota 20. They both support Ant+ and can read cadence and HRM (not speed, although they display speed from GPS). While similarly priced to the Edge 500, the price is a lot easier to justify because the device is a lot more versatile. The Edge series is very focused on cycling whereas the Dakota series is suited to a variety of activities. Jul 3, 2015 at 12:50
• @Kibbee I would be careful just because something is Ant+ doesn't mean it will record the power readings. The Cycleops power HR band sends both an HR and a power reading. My old edge 305 is ant+ but doesn't read power, same with most of the of the Garmin watches. I assume a non-cycling GPS may not look either. I have no idea about Ant+ phones. Software limitations yes, but limitations nonetheless. Jul 3, 2015 at 14:42

The short answer is no, there is no standard equivalent for effort between distance and elevation.

Of course, as others have mentioned, they are connected by the amount of effort you put in. But as you ride faster on the flat, the power required to drive you along rises as the square (some say the cube) of your speed. So riding 10% faster takes 20% to 30% more effort. This is mostly down to wind resistance, but rolling resistance plays a part too.

On a hill, your (well, at least my) speed is lower. Lets say you're climbing at 10kph (6mph). So the wind resistance is way lower (less than 1/6th) than the resistance you would have at 25kph (15.6mph). The main work (5/6 of the effort if you're producing the same power) you're doing is levering yourself up the hill. If you go 10% faster then the wind resistance still rises by 20% or so, but the effort of getting up the hill rises linearly.

So the point is, it's complicated. That's why there's no equivalence.

This is why, if you look at Strava or other tracking apps, they distinguish distance and elevation. They also distinguish time in the saddle, because measures something else: endurance.

For a real example, take a couple of my own rides.

• Today I rode an out and back course over 28 km (17.5 mi) with 650 m (2132 ft) of climbing. It's an undulating course averaging about 2.3% I averaged 25.3 kph (15.8 mph), similar to your pace. While not flat, it is compared to the next ride ...

• In the summer (it's winter here now) I climbed a hill. It's 1100 m (3600 ft) of solid climbing in 17 km (10.6 mi). It averages 6%, with pitches up to 24%. It took me 1 hour 45 minutes, for an average speed of only 9.7 kph (about 6 mph)!

There are two things about these rides. They show that I'm just a cyclist of modest abilities, so such comparisons should be relevant to you and many others. They also show the effect of continuous climbing, the effect of steeper hills, and the effect of longer duration, all tangled together.

It's complicated.

• +1 for modestly claiming a climb of 1,100m as a hill, when by all definitions that is mountain. The biggest mountain in the UK is just over 200 meters higher at 1,344. The tallest mountain in England is only 978m tall. feel ashamed now that the biggest hills in range of me are around 220m Jul 3, 2015 at 13:32
• It's complicated but not terribly so if you know power and speed. That's the basis for the "virtual elevation" approach for estimating cycling drag -- it converts effort (in terms of power and speed) into elevation gain. Jul 3, 2015 at 14:53
• @Cearon Lol :-) I just didn't want people imagining it was a big tough climb like we'll see in the TDF. Jul 3, 2015 at 14:55
• @andy256 its only (only! lol) 700 meters shy of Alpe D'huez... The 6% is a little tamer but still Chappeau for riding it. Makes me being proud of getting up some of our ~200m 9% climbs around here seem pathetic. Jul 3, 2015 at 14:58
• Maybe some day I'll climb a "hill" thats 3600 feet lol. Around here, the best I have is 13% grade 472 feet climb (144m). I guess I'll just ride that up and down a few times ;) its a fun one Jul 3, 2015 at 19:50

It really depends on speed. If you go slow (and there is no headwind) then riding on the flat is almost effortless (rolling friction is a very small factor with properly-inflated road tires). What slows you on the flat is wind resistance, and the faster you go the more wind resistance you face.

On the other hand, climbing a hill of a given height consumes a fixed amount of energy regardless of how fast you do it (once you factor out wind resistance), and, in theory, regardless of how steep the climb is (though of course once the hill gets too steep to climb "theory" falls apart).

You can probably come up with a way to convert a given % climb rate into an equivalent headwind for you and your bike, but there's no way to convert % climb into level miles with any degree of meaningfulness. At best you can come up with a conversion factor that assumes a given speed or energy output. And this would obviously be different for every rider.

• Sure there's a way to convert % climb into level miles. All you need to know are a handful of things: your total all-up mass (including you, your bike, and all your equipment), your coefficient of rolling resistance, your coefficient of aerodynamic drag, the wind speed, and your ground speed. Jul 3, 2015 at 14:49
• @R.Chung - My point is that you have to factor in speed, so it's not a simple equivalent between climb and miles. Jul 3, 2015 at 18:06
• So I need a way to calculate my resistance (and by that you mean friction between the tire and ground and the wheel and whatever it's attached to?), my drag, and the wind at any given moment? Sounds.....too complex haha Jul 6, 2015 at 17:29
• @TomSterkenburg - You don't need to know "rolling resistance" for standard (non-fat) tire bikes, since it's so small it can be ignored. Wind resistance is the biggie. And wind resistance is very greatly dependent on speed. Jul 6, 2015 at 20:04
• Calculating that alone is another ordeal, since I need to know my speed and the wind speed and direction (average across time). Would be fun to figure out, but I'm not sure if worth the effort lol Jul 6, 2015 at 20:39

It depends on other factors as well. A big one is speed. When you climb a hill, there is a minimum energy expenditure to get up the hill. On the flat, there is almost no minimum, but riding 10 mph is much easier than 15 mph (or whatever range of speeds is suitable for you). If you climb hills fast, you will get tired quickly.

Elevation gain can be measured in various ways as well. If you use Strava or MapMyRide to tell you that you have gained 500 feet, that is much less than looking on a map and finding you got 500 feet above where you started. The apps add up all the little ups along the way, so may report 1500 feet of climb when your altitude is just up 500 feet. You have to get used to it.

If you want to use your own figures from strava or some other program you can easily get get a feeling for the relative effort between biking a certain distance on the flat and on a grade. Use this calculator....http://bikecalculator.com/

For example I have a 2 mile hill at 5% which my best average speed is 9.3 mph. Entering the data gives me a calorie total of 185 calories. If I bike that same distance at a 0% grade at 20mph it gives me 68 calories. All of which feels about right to me, although if you asked I would have guessed that biking the 5% is easily 3 times harder.

For fun to see how fast I would have to go on the flat to equal the 185 calories at 5% I got 36mph, something I cant do for 1 second much less 2 miles.