Every number on FirstFiveK comes from a short list of formulas and one fixed training plan. This page lists all of them, says which parts are established fact and which are our own choices, and names the sources. If you can reproduce a figure with a calculator and get something different, tell us — the corrections page shows what happens next.
The plan itself
The 27 sessions follow the widely used couch-to-5K style progression: three sessions a week for nine weeks, moving from eight 1-minute runs to 30 minutes without stopping. The NHS describes its own version the same way — a programme that builds to running for 30 minutes, completed in 9 weeks or longer. We typed the minute structure in by hand; no text was copied from any published version, and the explanations on each page are our own.
We add two fixed walks to every session: 5 minutes before and 5 minutes after. They are included in every “total minutes” and “whole session” figure.
Pace, speed and time
Pace is seconds per mile. Everything else is arithmetic on that one number.
| Figure | Formula | Example at 13:00 per mile |
|---|---|---|
| Treadmill mph | 60 ÷ pace in minutes | 60 ÷ 13 = 4.6 mph |
| Treadmill km/h | mph × 1.609344 | 7.4 km/h |
| Pace per km | pace per mile ÷ 1.609344 | 8:05 per km |
| 5K time | pace × 3.10686 miles | 40:23 |
| Distance in a run | minutes ÷ pace | 30 min = 2.31 miles |
The mile is exactly 1,609.344 metres. That follows from the international foot, which NIST defines as exactly 0.3048 metre, times 5,280 feet. A 5K is 5,000 metres, or 3.10686 miles. Speeds are rounded to one decimal because that is what treadmill displays show; times are rounded to the nearest second.
One consequence appears all over the site: 30 minutes of running equals 5K only at about 9:39 per mile (1,800 seconds ÷ 3.10686). At any slower pace the plan’s final run ends before 5K does. We treat that as a fact to plan around, not a failure.
Session distance and the 18:00 walking reference
A session’s distance is running minutes ÷ running pace, plus walking minutes ÷ walking pace. Walking minutes are the warm-up, every walk break and the cool-down.
Walking pace is our own assumption: 18:00 per mile (3.3 mph) for everyone. We chose a single value so that tables are comparable across paces. It sits inside the range the US physical activity guidelines use for brisk walking — the Physical Activity Guidelines for Americans give 2.5 to 4 mph as moderate-intensity walking. If you walk faster or slower, the walking part of each distance shifts in proportion; the running part does not change. The distance table and its CSV use this same reference.
“Too slow” and the talk test
We do not grade paces. Where a page says a pace is fine for the plan, the test behind it is the talk test the CDC describes for measuring intensity: at moderate effort you can talk but not sing. The pace bands in the chart (quick beginner, steady jog, easy jog, gentle jog, jog-walk) are labels we wrote to make the table easier to scan. They are not standards from any organisation.
The restart rule
The restart table is a rule of thumb written by this site. It is not a clinical guideline and we do not present it as one.
| Time off | Restart from |
|---|---|
| 1 week | the week you were on |
| 2 weeks | one week back |
| 3 weeks | two weeks back |
| 4 weeks | three weeks back |
| 5–6 weeks | half the week you had reached, rounded up |
| 8 weeks or more | week 1 (week 2 if you had reached week 7 or later) |
The rule is deliberately cautious. Its only goal is that the first session back is one you can finish. It applies to breaks for ordinary reasons — travel, work, lost motivation. After illness or injury, a doctor’s advice replaces this table.
What we do not do
- No invented authors, reviewers or credentials. Pages are written by the FirstFiveK team and say so.
- No medical advice. Nothing here diagnoses, treats or predicts anything about your health.
- No figures without a formula. If a number is on a page, it comes from this list.
Checking and corrections
A script recomputes every table from the formulas above on each build and compares it with an independent calculation; a mismatch stops the site from publishing. Each page carries a “last checked” line with what changed. Errors that readers report are fixed and logged, with dates, on the corrections page.