Minetti Slope Calculations

Hills and bridges are where groups break apart. Runners attack the climb, burn fuel, then fly down the other side and pay for it later. A good pacer runs even effort, not even speed. This lesson shows how to turn that idea into numbers you can use.

How much harder is a slope?#

The Italian scientist Alberto Minetti measured how much energy runners use per metre on different slopes. His results are summed up in a formula for the energy cost C of running one metre on a gradient i (written as a decimal, so a +4% climb is 0.04 and a −3% descent is −0.03):

C(i) = 155.4i⁵ − 30.4i⁴ − 43.3i³ + 46.3i² + 19.5i + 3.6

On flat ground (i = 0) the cost is 3.6. Dividing by this gives the Grade Adjustment Factor (GAF):

GAF = C(i) ÷ 3.6

A GAF of 1.24 means "this kilometre takes about 24% more effort than a flat one".

Worked example#

Flat target pace 5:00/km (300 s), slope +4%:

• C(0.04) ≈ 4.451
• GAF = 4.451 ÷ 3.6 ≈ 1.236
• 300 s × 1.236 ≈ 371 s, so 6:11/km for the same effort

Why pacers damp the numbers#

The raw GAF describes energy cost in a laboratory. Applied directly to a race group it overstates the real pace changes. Slowing to 6:11 on a short climb would scatter the group, and running 3:37/km downhill would be reckless and hard on the legs.

So pacers use a damped factor:

P_adj = P × (1 + k × (GAF − 1))

• P is the flat target pace.
• k is a damping factor, usually around 0.3–0.5.
• Downhill gains are capped at about 5% faster than flat pace.

With k = 0.4 and a 5:00/km flat pace:

For +4%: 1 + 0.4 × 0.236 = 1.094, and 300 s × 1.094 ≈ 328 s, so 5:28/km instead of 6:11/km. The Elevation calculator does this for every segment of your course.

Protect the finish time#

Slowing on climbs costs time, and that time has to come from somewhere. The rules:

• Plan it in advance. Build the slope targets into the split plan so the segments still add up to the target finish time. The Split planner can do this for you.
• Bank nothing on downhills. Use a descent only to return smoothly to your planned schedule, never to get ahead of it.
• Absorb the rest on the flat. Time lost on a bridge is recovered gradually over the following flat road, within about 5 s/km (see adjusting pace smoothly).

Key takeaways#

• GAF = C(i) ÷ 3.6; a +4% slope gives GAF ≈ 1.236, turning 5:00/km into 6:11/km at equal effort.
• Raw GAF overstates real pace changes, so use P × (1 + k(GAF − 1)) with k ≈ 0.3–0.5.
• Cap downhill speed-ups at about 5% faster than flat pace.
• Run even effort, not even speed, but bank nothing on the downhills.