What does a 1%, 2% or 3% negative split mean?

What the percentage measures

The split calculator and the race charts on this site define the split as:

split % = (first half time - second half time) / finish time x 100

A positive number is a negative split (the second half is quicker). So for a 4:00:00 marathon (14,400 seconds) at 2%, the halves differ by 2% of 14,400 = 288 seconds. They must still add up to 14,400, so the first half is 7,200 + 144 = 7,344 seconds (2:02:24) and the second is 7,200 - 144 = 7,056 seconds (1:57:36).

Two consequences follow straight from that definition, and they hold at any distance:

• The first half is p% slower than an even-paced half. At 2%, 7,344 / 7,200 = 1.02.
• The gap between the halves is p% of the whole race, which is twice p% of either half. A "1% negative split" sounds tiny; on a marathon it is a 2:24 gap at 4:00 and a 3:00 gap at 5:00.

Halfway times for common races and goals

Computed with the site's engine (RUN.timeAt at half the distance). The even-pace halfway time is simply half the goal.

Halfway times like these are the most useful numbers for race day, because the half mat is one checkpoint every course has and every runner passes.

How the site's model spreads the change

A negative split could be run as two blocks: one steady pace for the first half, a quicker steady pace for the second. The split calculator does something smoother. It lets pace change in a straight line with distance, slowest at the start and quickest at the finish, with the change spread evenly over every metre. In engine terms, the pace at distance x is:

pace(x) = a + b(x - D/2), with a = T / D and b = -(p / 100) × 4T / D²

where T is the finish time, D the distance and p the split percentage. Integrating that pace from the start to any point gives the elapsed time there, which is what RUN.timeAt returns. Three properties drop out of the algebra:

• Pace at halfway equals the even pace. At x = D/2 the second term is zero.
• The start is 2p% slower than even, the finish 2p% faster. At x = 0, pace = a(1 + 2p/100). For a 4:00 marathon at 2% that is 9:31.2 per mile at the gun, falling to 8:47.3 at the line, around an average of 9:09.2.
• You are furthest behind an even schedule at halfway. Before halfway every metre is slower than average, after it every metre is quicker, so the deficit builds until the half mat and then shrinks to zero at the finish. At 2% on a 4:00 goal the deficit is 144 seconds at halfway, 104 seconds at 10 km and 118 seconds at 30 km.

That last point matters for nerves: at the halfway mat a correctly run negative split looks like the worst moment of the race on the clock. It is the plan, not a sign you have fallen behind.

First and last mile, against even pace

Because pace changes inside each mile, the split for a whole mile is the average across it. These are the first mile and the last full mile (before the final fraction) from RUN.splits:

Notice the 5K and 10K rows at the same 8:02.8 average. The same percentage gives a wider spread on the 10K (15.5 seconds between the first and sixth mile at 1%) than on the 5K (12.4 seconds between the first and third), because the change is spread over more distance and the first and last miles sit further from the middle.

"Start 10 to 25 seconds slower": what that is in percent

Seconds-per-mile advice is common on calculator sites. In this model the first mile's gap from even pace grows in direct proportion to the split percentage, so a fixed number of seconds means a different plan for every runner. For a marathon, the first mile is 7.9 seconds per 1% slower than even at a 3:00 goal, 10.6 seconds per 1% at 4:00 and 13.2 seconds per 1% at 5:00. So:

The same 25 seconds is a much bolder plan for a 3-hour runner than for a 5-hour runner. Choosing the percentage and letting the calculator turn it into seconds keeps the plan in proportion to your pace.

What changes against even pace, and what does not

The finish time does not change: every plan in the tables adds up to the goal exactly. What changes is where the time is spent. On a 4:00 marathon a 2% plan asks for 21.1 seconds per mile slower than even in the first mile and 20.8 seconds per mile faster in the last full mile. If the second half does not come, the deficit at halfway (144 seconds) is the amount you would have to find later just to break even.

Even pace is the zero row of the same model, so you can compare them directly in the marathon pace chart or the half marathon pace chart, which offer 1 to 3% negative and 1 to 2% positive splits on every goal. The pace band generator prints whichever plan you choose, with the elapsed time at each marker, so you are checking against the plan you picked and not against even pace.

A positive split is the mirror image

A positive split (a negative percentage in the formula) reverses everything: a quicker start, a slower finish, and you are furthest ahead of even pace at halfway. The halfway times in the first table simply swap: a 4:00 marathon at a 2% positive split goes through halfway in 1:57:36 and needs 2:02:24 for the second half. Planning one on purpose is unusual, but it is a handy way to see what a fast start costs: every second banked before halfway in this model is paid back after it.

Limits of the model

A straight-line change in pace is a planning convenience, not a description of how anyone actually runs. Real splits jump around with hills, wind, crowds and drinks; on a hilly course the course pace planner spreads time by the energy cost of each slope instead, and the uphill pace guide shows how large those swings are. I make no claim here about which split strategy is fastest; the tables only show what each percentage means. Distances are the exact race lengths, so the marathon rows use 42.195 km (see how long a marathon really is).

Build your own plan: split calculator, marathon pace chart, pace band generator.

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