Running pace + race time calculator

Pace math — Riegel's formula and Daniels' training zones

Two pieces of running math, packaged together:

1. Race-time prediction (Riegel)

T₂ = T₁ × (D₂/D₁)^1.06

You can't run 26.2 miles at 5K pace — fatigue makes you slower as distance grows. Pete Riegel's 1981 formula models this with the 1.06 exponent (the 'fatigue factor'). It's accurate within 2-3% for distances 1.5× to 4× of the reference race.

A 22:30 5K → ~3:30 marathon predicted. Caveat: only accurate if you've trained for the longer distance. A 22:30 5K runner who hasn't built endurance will run 4:00+ marathon despite the prediction.

2. Training paces (Daniels)

Jack Daniels' VDOT system maps current race performance to training paces:

• Easy (~130% of race pace): aerobic base, recovery, long-run majority. Should feel conversational.
• Marathon pace (~115%): rehearsal pace for actual marathons.
• Tempo / threshold (~110%): "comfortably hard," 20-40 min sustained.
• Interval / VO2 (~96%): 3-5 min reps at this pace, equal recovery.
• Repetition (~90%): 200-400m bursts, full recovery.

The percentages are off the 5K pace because 5K is a near-VO2max effort (~95-98% of VO2 max for trained runners). Calibrating off marathon pace is less reliable because marathon performance is endurance-limited, not VO2-limited.

How to use this

Run easy days slow enough. Most amateur runners run easy days at tempo pace and tempo days at easy pace — the dreaded "gray zone." The prescribed easy pace from this calculator should feel almost too slow. That's the point.