Incline Pace Calculator
The flat-ground pace with the same oxygen cost as your treadmill speed at an incline, from the ACSM running and walking equations. Pace per km and per mile, VO2 and METs.
Result…
How it's calculated
Speed (m/min) = km/h × 1000 ÷ 60, or mph × 1609.344 ÷ 60 Running: VO2 = 0.2 × speed + 0.9 × speed × grade + 3.5 Walking: VO2 = 0.1 × speed + 1.8 × speed × grade + 3.5 (VO2 in mL/kg/min, grade as a fraction, 5% = 0.05) Flat equivalent: running speed × (1 + 4.5 × grade); walking speed × (1 + 18 × grade) METs = VO2 ÷ 3.5
Running or walking uphill costs more oxygen than the same speed on the flat. The American College of Sports Medicine (ACSM) metabolic equations split the cost into three parts: a horizontal part (speed × 0.2 for running, × 0.1 for walking), a vertical part (speed × grade × 0.9 for running, × 1.8 for walking) and 3.5 mL/kg/min for rest. Setting the uphill cost equal to a flat cost gives the flat speed that takes the same effort, which is what this calculator shows as a pace. It is useful for matching a treadmill hill session to a road pace, or for planning an incline walk. The equations are for steady, level or uphill work, not downhill.
Your numbers, step by step
About the Incline Pace calculator
This incline pace calculator finds the flat-ground pace that costs the same oxygen as your treadmill speed at a given incline. It uses the American College of Sports Medicine (ACSM) metabolic equations: for running, VO2 = 0.2 × speed + 0.9 × speed × grade + 3.5, and for walking, VO2 = 0.1 × speed + 1.8 × speed × grade + 3.5, with speed in metres per minute and grade as a fraction. Both equations are set out in this study of the ACSM equation in athletes. Setting the uphill cost equal to a flat cost gives a flat speed of speed × (1 + 4.5 × grade) for running, or × (1 + 18 × grade) for walking. Runners use it to match a hill session to a road pace, and walkers to see what an incline walk is worth. Results come per km and per mile, with VO2 and METs, and the steps show each term.
How to use it
- Choose “Running” or “Walking” under “You are”, since ACSM uses a different equation for each.
- Pick the “Speed unit”, km/h or mph, to match your treadmill.
- Enter the “Treadmill speed” and the “Incline (grade)” in percent.
- Read the “Equivalent flat pace” per km and per mile, plus the oxygen cost and METs.
- Use the chart to see how the flat equivalent grows as the incline rises at the same speed.
Worked example
A runner sets the treadmill to 9 km/h at a 6% incline. The speed is 9 × 1000 ÷ 60 = 150 m/min, so VO2 = 0.2 × 150 + 0.9 × 150 × 0.06 + 3.5 = 30 + 8.1 + 3.5 = 41.6 mL/kg/min, about 11.9 METs. The flat speed with the same cost is (41.6 − 3.5) ÷ 0.2 = 190.5 m/min, or 11.43 km/h. That is a flat pace of 5:15 per km (8:27 per mile), against a treadmill pace of 6:40 per km: the incline adds 27% to the effort.
Updated
Questions people ask
How do I convert a treadmill incline to a flat running pace?
Multiply the treadmill speed by (1 + 4.5 × grade), with the grade as a fraction, then turn that speed into a pace. At 10 km/h and 5%, the flat speed is 10 × 1.225 = 12.25 km/h, a pace of 4:54 per km.
What is the ACSM running equation?
VO2 = 0.2 × speed + 0.9 × speed × grade + 3.5, in mL/kg/min with speed in metres per minute. The 0.2 term is the cost of moving forward, the 0.9 term the cost of climbing, and 3.5 is the resting cost. Dividing VO2 by 3.5 gives METs.
Why is the walking result so much faster than I could walk?
Walking uphill costs relatively more than running uphill, so the walking equation multiplies the grade by 18 rather than 4.5. A steep walk can match the oxygen cost of a flat speed you could only run. The calculator compares walking with walking; it does not give you a running pace.
Does a 1% incline make a treadmill feel like running outside?
The ACSM equations leave out air resistance, so they cannot say what incline makes up for it. They only compare uphill with level treadmill work. For pacing a road run from a time and distance, use the pace calculator.
What are the limits of an equivalent flat pace?
The equations estimate an average person's steady-state oxygen cost, so your own cost depends on fitness, form and body build. They are for level or uphill work, not downhill, and are least accurate at the extremes of speed and grade. If you have a heart condition or other health concern, ask a doctor before hard hill sessions.