TRIMP

TRIMP, short for training impulse, is a single number for how much physiological work a session cost you, calculated by multiplying how long you trained by how hard your heart was working. Eric Banister's group introduced it in the 1970s as the input to a model of fitness and fatigue, and the heart rate training load scores on many watches and apps, including Titan's, descend from it.

A 60-minute easy run and a 25-minute set of hill repeats can leave you equally tired. Minutes alone rank the easy run higher. Average heart rate alone ranks the hills higher. TRIMP combines the two so you can add sessions of different kinds into a daily and weekly total, and then compare this week with the weeks before it.

01Where TRIMP came from

Banister, Calvert, Savage and Bach described a systems model of training in the Australian Journal of Sports Medicine in 1975, and Calvert and the same group published the indexed version in IEEE Transactions on Systems, Man, and Cybernetics in 1976. They borrowed the idea from control engineering. Each training session is an impulse fed into the athlete, and performance is the output. To run the model, they needed that impulse as a number, and TRIMP is that number.

Morton, Fitz-Clarke and Banister formalized the model in the Journal of Applied Physiology in 1990. Each impulse produces two responses, fitness and fatigue. Both decay exponentially when training stops, and fatigue decays faster. Predicted performance is a baseline plus a scaled fitness term minus a scaled fatigue term. For the two subjects in that paper, the fitted fitness time constants were 50 and 40 days and the fatigue time constants were 11 days for both, as tabulated by Kontro and colleagues in 2025. In practice, training platforms skip individual fitting and often use fixed constants of 42 days for fitness and 7 days for fatigue.

02Banister's exponential formula

Banister's TRIMP expresses intensity as the fraction of your heart rate reserve used during the session, then applies a weighting factor that rises exponentially with that fraction.

ΔHR ratio = (exercise HR − resting HR) / (max HR − resting HR)

TRIMP = duration in minutes × ΔHR ratio × a × e^(b × ΔHR ratio)

The constants come from the shape of the blood lactate curve. For men, a is 0.64 and b is 1.92. For women, a is 0.86 and b is 1.67. Maughan and colleagues reproduce both pairs from Banister's 1991 chapter on modeling elite athletic performance. The exponential term exists because blood lactate climbs steeply as heart rate approaches its maximum. Without it, a long session at low intensity would receive too much weight relative to a short hard one, a correction Maughan and colleagues trace to the 1990 Morton paper.

Two consequences follow for your own numbers. First, every input moves the result. A resting heart rate recorded 10 bpm too high lowers the ΔHR ratio of a 150 bpm effort with a max of 190 from 0.714 to 0.692. Second, the formula was written for one average heart rate per session. Because the weight rises exponentially, the hard minutes of an interval session are worth more than their share of the average, so scoring the session from its mean heart rate understates it. Applying the formula minute by minute avoids that, and the worked example below shows the size of the gap.

03Zone-based TRIMP from Edwards and Lucia

Banister's formula needs a resting heart rate, a maximum heart rate and an exponential calculation. Two simpler methods replace the curve with steps.

Edwards' method, from The Heart Rate Monitor Book in 1993, splits heart rate into five zones by percent of peak heart rate. Time at 50 to 60 percent counts 1 per minute, 60 to 70 percent counts 2, 70 to 80 percent counts 3, 80 to 90 percent counts 4, and 90 to 100 percent counts 5. Foster and colleagues used exactly those zones as their objective reference in 2001. Heart rate below 50 percent falls outside every zone and adds nothing.

Lucia and colleagues used three zones anchored to each rider's own lab test when they compared the loads of the Tour de France and the Vuelta a España in 2003. Phase I sits below the ventilatory threshold and counts 1 per minute. Phase II sits between the ventilatory threshold and the respiratory compensation point and counts 2. Phase III sits above the respiratory compensation point and counts 3. Across seven professional cyclists, the Tour took significantly longer, 5,552 minutes against 5,086, yet the total loads of the two races did not differ. The Vuelta packed a similar load into less time, so its minutes carried more weight on average.

Edwards' zones need only a max heart rate, and the same percentage can sit at different metabolic points for two athletes. Lucia's zones need a lab test with gas analysis, and they sit at the same metabolic landmarks for every athlete. Maughan and colleagues note that Lucia's cap of 3 may undercount players who spend long stretches well above threshold, and that Edwards' large integer steps blunt small changes in load.

04Session RPE, the method without a heart rate monitor

Carl Foster's session RPE method multiplies a single rating of how hard the whole session felt by its duration in minutes. You rate the session on a 0 to 10 category ratio scale about 30 minutes after it ends, a delay Foster's group chose so that an easy cooldown or a brutal final interval would not dominate the answer. A 60-minute session rated 5, labeled hard on Foster's version of the scale, scores 300 arbitrary units.

Foster and colleagues tested it against Edwards' zone method in 2001 during steady and interval cycling and during basketball. The two tracked each other consistently, but session RPE always produced the larger number, so the two are not interchangeable. In 479 soccer training sessions, Impellizzeri and colleagues found that individual correlations between session RPE and the Edwards, Banister and Lucia methods ranged from 0.50 to 0.85.

Session RPE is most useful where heart rate is least useful. Foster's group wrote that resistance training and plyometrics cannot be evaluated objectively with heart rate criteria. Day and colleagues then showed in 2004 that session RPE separated heavy, moderate and light lifting sessions with an intraclass correlation of 0.88 across repeated trials. One set of 4 to 5 repetitions at 90 percent of one-repetition maximum was rated harder than one set of 15 at 50 percent.

Apple adopted the same idea in watchOS 11. After each workout, Apple Watch shows an effort rating from 1 to 10, estimated automatically for popular cardio workouts from heart rate, GPS, elevation, age, height and weight, and entered by hand for workouts like strength training. Apple's Training Load combines effort ratings and duration into a 28-day weighted average and compares your most recent 7 days with it.

05A worked calculation

Take a 30-year-old man with a resting heart rate of 50 bpm and a max of 190 bpm. He runs for 60 minutes. The first 15 minutes average 130 bpm, the middle 30 average 150 bpm, and the last 15 average 170 bpm. For the Lucia column, assume a lab test put his ventilatory threshold at 145 bpm and his respiratory compensation point at 165 bpm. He rates the run a 5.

The Banister numbers come from the ΔHR ratio at each segment. At 130 bpm the ratio is 80 divided by 140, or 0.571, and the weighted minute is 0.571 × 0.64 × e^(1.92 × 0.571), about 1.10. At 150 bpm each minute is worth about 1.80, and at 170 bpm about 2.84. Fifteen minutes in the top segment count for about four fifths as much as thirty in the middle. Collapsing the run to its mean of 150 bpm loses about 4 percent.

For Titan, a max of 190 puts Zone 1 at up to 139 bpm, Zone 2 at 140 to 152, and Zone 4 at 164 to 175 bpm. The first segment scores 1 a minute, the middle 2, the last 4.

The seven scores range from 108 to 300 for one run. Each is internally consistent, and none can be compared with another. A TRIMP only means something next to other TRIMPs computed the same way for the same person.

06What your number means

No population normal range exists for TRIMP, and none could. The units change with the method, the constants change with sex, and the result depends on the max and resting heart rates behind it. A well-trained runner and a beginner can both log 120 for sessions that cost them very different amounts.

Your own history is the reference. A single session score tells you how this workout compared with your other workouts. The useful signal comes from the running totals. A short-term average stands in for fatigue and a long-term average stands in for fitness, and the gap or ratio between them shows when recent training has run ahead of what you are used to. The acute to chronic workload ratio entry covers that ratio and the argument over its injury thresholds, and the training load blog post walks through a full week.

Watch for jumps that do not match what you did. If a routine easy run suddenly scores 30 percent higher, check for a changed max heart rate, a loose watch band, or a hot day before assuming the run was harder.

07How wrist heart rate affects TRIMP

Every heart rate TRIMP inherits the error of its heart rate data. In a Stanford study of 60 adults wearing seven wrist devices, the Apple Watch had the lowest overall heart rate error, and six of the devices had a median heart rate error below 5 percent during cycling. Error was higher during walking than cycling, and higher in men, at greater body mass index, and with darker skin tone. A Duke study of optical sensors in 2020 found no significant difference in accuracy across skin tones, but absolute error during activity averaged 30 percent higher than at rest, and devices differed most in how they followed rapid changes in activity.

Apple states that rhythmic movements such as running or cycling give better readings than irregular movements such as tennis or boxing, that cold can reduce skin blood flow at the wrist below what the sensor needs, and that some tattoos block the sensor's light. Apple Watch can also pair with a Bluetooth chest strap.

For TRIMP, the effect depends on the session. Steady runs and rides get accurate heart rate and therefore accurate load. Short intervals, boxing and cold-weather sessions carry the most error. Zone methods feel that error only when it pushes minutes across a zone boundary.

08Known limitations

Sex coefficients

Banister's constants encode average blood lactate curves for men and for women. In the worked example, the same heart rate data scores 113 with the male constants and 126 with the female constants, about 12 percent more, for the same run. Neither curve belongs to any individual. Manzi and colleagues built individual weightings from each runner's own heart rate and lactate profile in 2009. Across eight recreational distance runners over 8 weeks, weekly individualized TRIMP correlated with gains in running speed at 2 mmol/L lactate (r = 0.87) and at 4 mmol/L (r = 0.74). With group-average weightings, no significant relationship appeared. Zone methods such as Edwards' and Titan's skip the sex constants entirely, so they give the same score for the same heart rate regardless of sex.

Strength and intermittent work

Heart rate tracks the cardiovascular cost of exercise. Much of the cost of a heavy set of three squats falls on muscle and connective tissue instead. Foster's group wrote that heart rate cannot objectively evaluate resistance training or plyometrics, and session RPE remains the better tool there.

Intermittent sport breaks the lactate curve that the Banister weights depend on. Akubat and Abt matched 12 team sport players for distance and mean speed in continuous and intermittent running. The intermittent trials produced higher blood lactate at 75 and 100 percent of the speed at VO2max and higher TRIMP weightings at high heart rates. Weightings derived from a continuous test may underestimate the dose of intermittent training and matches.

Heat, dehydration and cardiac drift

Heart rate climbs during long exercise at a fixed workload, especially in heat. Wingo and colleagues had nine male cyclists ride at 60 percent of VO2max in 35 °C heat. Between minutes 15 and 45, heart rate rose from 151 to 169 bpm at the same power, a 12 percent increase. Over the same half hour, VO2max fell 19 percent, so the same power output demanded 78 percent of the rider's reduced VO2max, up from 63 percent. Some of that extra TRIMP is real strain. Dehydration adds to it. Montain and Coyle found that the rise in heart rate across 2 hours of cycling in 33 °C heat was linearly related to how much body mass the riders lost.

A summer long run can therefore score higher than the same run at the same pace in October. Titan counts that extra heart rate as extra load. If you are comparing fitness across seasons, compare pace or power at a given heart rate as well.

Day-to-day heart rate noise

Halson's 2014 review puts day-to-day variation in submaximal heart rate as high as 6.5 percent and advises controlling for hydration, environment and medication. At 150 bpm, a 6.5 percent swing is about 10 bpm, close to the width of a Titan zone. A steady session near a boundary can land in a different zone from one day to the next with no change in effort.

09How Titan computes training load

Titan uses a five-zone TRIMP close to Edwards' method, with zones set as percentages of max heart rate and each minute weighted by its zone number. The training load help article lists the weights and constants.

Titan's max heart rate is the higher of the top heart rate in Apple Health over the last 30 days and 220 minus your age, unless you set a custom max. Default zones start at 53, 74, 81, 87 and 93 percent of that max, as the heart rate zones article describes. The max heart rate and heart rate zones glossary entries explain why that anchor matters.

For each workout, Titan averages heart rate within each minute and assigns the minute to a zone. A Zone 1 minute counts 1 and a Zone 5 minute counts 5. Titan's zone boundaries sit higher than Edwards', and heart rate below the Zone 1 start still counts as Zone 1, so no workout minute scores zero. Like Edwards, Titan uses no resting heart rate and no sex constant. Only heart rate recorded inside a workout counts, so a stressful afternoon adds nothing.

Workouts without heart rate data still count toward load. For those, Titan multiplies the workout's minutes by an activity factor. Endurance workouts count 1.0 per minute, mixed-intensity 0.95, strength 0.9, mobility 0.65, other workouts with distance 0.95, other workouts without distance 0.8, and an Other workout renamed as sauna or steam 0.5. Titan does not read Apple's effort ratings, so a session RPE you enter on the watch does not change Titan's load.

Daily load then feeds two exponentially weighted averages. Short-term load uses a 7-day time constant and long-term load a 42-day time constant, the fixed pair Kontro and colleagues describe as common on training platforms. Each day short-term load moves about 13 percent of the way toward the day's load, and long-term load about 2.4 percent. Days without a workout count as 0. Titan starts the calculation 84 days before the first day it shows, so the chart's left edge reflects earlier training.

The load ratio is short-term divided by long-term load. Titan labels it Low below 0.8, Optimal from 0.8 up to 1.4, High from 1.4 up to 1.6, and Risk at 1.6 and above. In Trends, Training load focus splits the period's load into Low aerobic from Zones 1 and 2, High aerobic from Zone 3, and Anaerobic from Zones 4 and 5.

The same daily load drives the Exertion score. Workout points follow 10 × (1 − e^(−load / 100)), and steps add up to 1.2 points. The 135-point run in the worked example earns about 7.4 workout points before steps. The WHOOP Strain comparison sets this against WHOOP's approach.

The training load deep dive shows that Titan's integer weights fall within the spread of Banister's curve for resting heart rates from 40 to 65 bpm, and it covers the costs of a stepped scale. Two sessions a few beats apart can land in different zones, and a wrong max heart rate shifts every boundary at once.

10Using TRIMP well

Pick one method and keep it. Scores from different methods, devices or zone settings do not belong on the same chart. When you change your max heart rate or edit your zones in Titan, expect the history to shift and compare trends from after the change.

Read the trend more than single sessions. One high number is a hard workout. Several weeks of short-term load well above long-term load means your body is absorbing more than it is used to, and it is the pattern to watch for overreaching.

Pair heart rate load with how the session felt. Heavy lifting and team matches can feel crushing while scoring modestly, and a hot run can score high at an easy pace. When heart rate and feel disagree, record an RPE rating or a note alongside the number.

11References

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