There are roughly 1600 meters in a miles, so your 1500 meter time multiplied by 1600/1500, or 16/15, would give you a mile time. For example, a 6:00 1500 time would be a 6:24 mile.
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1 mile = 1608 meters, so they are pretty much the same
The mile run is not an Olympic event. The closest one is the 1500 meter run, which is 0.932 mile. At the time I write this ... end of July 2012 ... I don't know what will happen at London. The current Olympic record for that event was set at Sydney in 2000 by Noah Ngeny of Kenya, who ran 1500 meters in 3:32.07 .
One mile equals to 1 609.344 meters. Countries that use International System of Units that imported some contests such as a mile race or a quarter mile sprint rounded the mile to 1 600 meters and its quarter to 400 meters. For practical terms you might use the 1 600 m race time as the same as the one mile race time, but for precision you may use the full conversion rate bolded above.
A second is a time measurement, a meter is distance. There is no conversion.
"it depends on your pace, but it is only 100 meters short of a mile. So, add somewhere from 20 to 30 seconds."Adding 20 to 30 seconds doesn't take a runner's pace into consideration. When converting for qualifying standards, I use the following formula...1500 Meter time in seconds X 1.079709247 =converted mile time.For instance, a 4:00.00 1500 meter time would be converted by doing this...convert 4:00 to seconds. This would give you 240.00 seconds...Then240.00 x 1.079709247 =259.13... This is a 4:19.13 Mile(the exact conversion of 1500 meters to 1609.343998 meters would use 1.072895999, but we assume that you slow a bit the longer your run.)Using 1.0797 or about 1.08 allows for some slowing but it may not be enough. An interesting way to look at it is to compare the world records for both races. Interestingly at the current time the world record for both events (for men) is held by HichamEl Guerroujwho set the 1500 m. record in July 1998 in Rome at 3:26.0 and the following summer (July 1999) set the 1 mile record of 3:43.1 at the same stadium. The ratio is 1.083, only slightly greater than the 1.0797 suggested above. But the relative slowing over the extra 100 meters may be greater the slower one is running. Also the mile run is not run so frequently as the 1500 meter run so the 1500 meter record should advance more rapidly and make the comparison less valid. Some evidence for the greater relative slowing over the extra 100 meters at a slower pace is that the ratio for the women's world records in the two events is 1.096. But in that case it is 2 different women a few years apart at different tracks so hardly definitive. Using 1.08 to 1.10 seems a reasonable range for a conversion factor for elite to veryfast middle distance runners.