Target Heart Rate Calculator (Karvonen Formula)
Solve the Karvonen formula THR = ((HRmax − HRrest) × intensity) + HRrest for any of its four variables — the target heart rate, maximum heart rate, resting heart rate, or training intensity — with step-by-step algebra, a live heart-rate-reserve gauge, and a full breakdown of all five training zones.
Karvonen beats %HRmax for trained athletes
The simple %HRmax method calculates the target as a percentage of maximum heart rate alone — 70% of 185 is 129.5 bpm. The Karvonen method instead works from the reserve between rest and maximum — 70% of (185 − 60) + 60 = 147.5 bpm. The 18 bpm gap is not a rounding error: it reflects the fact that a fitter person with a lower resting HR has a wider usable range, and the same perceived effort occurs at a higher absolute heart rate. This is why Karvonen is the standard method in exercise physiology.
Resting HR is the anchor that personalises everything
Two people with the same HRmax but different resting HRs have very different training zones. A 40-year-old with HRmax 180 and HRrest 45 (a trained runner) has a reserve of 135 bpm and a 70% target of 139.5 bpm. A sedentary 40-year-old with the same HRmax and HRrest 75 has a reserve of 105 and a 70% target of 148.5 bpm. The sedentary person reaches "70%" at a higher absolute rate because their usable range is narrower. This is why measuring resting HR — best done on waking, before getting out of bed — matters so much.
The five zones come from splitting the reserve
Standard training zones divide the heart-rate reserve into five bands of 10 percentage points each: 50–60% (Zone 1), 60–70% (Zone 2), 70–80% (Zone 3), 80–90% (Zone 4) and 90–100% (Zone 5). Each band corresponds to a physiological state and a fuel mix. Zone 2 sits at the top of fat oxidation, Zone 3 is the aerobic sweet spot for endurance, Zone 4 is at lactate threshold, and Zone 5 is at VO₂max. Splitting the reserve rather than splitting the raw HRmax gives bands that are physiologically comparable across individuals.
Intensity above 100% is not physically meaningful
Setting intensity above 100% of heart-rate reserve would imply a target above HRmax, which the heart cannot sustain — this is why the intensity slider caps at 100%. Below about 30%, the target drops close to resting HR and the workout is really just rest. For most steady-state training, the useful intensity range is 60–85%. Interval work may briefly touch 90–95%, but only for seconds at a time. The Karvonen formula describes sustainable targets; it does not model the heart-rate dynamics of short, high-intensity intervals.
How to Use This Calculator
The Karvonen formula links four quantities: target heart rate, maximum heart rate, resting heart rate and training intensity. Fill in three and the calculator solves for the fourth.
1. Enter HRmax and HRrest
If you don't know your HRmax, estimate it as 220 − age or use the Maximum Heart Rate Calculator on this site. Measure resting HR on waking, before getting out of bed, over three mornings and average them.
2. Choose your intensity
Pick the percentage of heart-rate reserve that matches your goal. Recovery is 50–60%, aerobic base is 60–70%, aerobic training is 70–80%, threshold is 80–90%, and maximum is 90–100%.
3. Read the result and zone strip
The result card shows your target heart rate for the chosen intensity, plus a five-chip zone strip with the bpm range for every zone so you can see where you sit.
4. Solve for other variables
Switch the "Solve for" toggle to work backwards: given a target you want to hit, find the intensity that produces it; given a heart rate you observed, find what zone it corresponds to.
5. Check the gauge and charts
The gauge diagram shows your HRrest, HRmax and THR on a single heart-rate-reserve scale, and the charts plot THR against intensity and against HRmax.
6. Switch to Advanced for depth
Advanced mode adds charts of THR vs. HRmax and THR vs. HRrest, a comparison against the simpler %HRmax method, a sensitivity check on each input, and companion metrics including estimated sustainable durations.
What This Tool Offers
Built around the Karvonen formula THR = ((HRmax − HRrest) × intensity) + HRrest, the standard method for personalised training zones.
Four-way solving
Solve for target heart rate, maximum heart rate, resting heart rate, or intensity. The calculator rearranges the Karvonen formula for whichever variable you choose.
Heart-rate-reserve gauge
A live gauge showing HRrest and HRmax as anchor points, the reserve between them, the five zone bands, and a marker for your current THR.
Zone verdict
Every result is classified into one of the five standard training zones — recovery, aerobic base, aerobic, threshold, or maximum — with a colour-coded badge and full description.
%HRR converter
Enter a heart rate and see what percentage of your reserve it corresponds to — the fastest way to check whether a live reading is in the zone you intended.
Five coordinated charts
THR vs. intensity, a reserve gauge, THR vs. HRmax, THR vs. HRrest, and a direct comparison of Karvonen against the simpler %HRmax method.
Reference tables
A full zone reference with bpm bands at your current values, a THR lookup grid across intensities, a %HRR conversion table, and a complete variable reference.
Reference Tables & Conversions
A %HRR converter, a THR lookup grid, and a training-zone reference table.
Heart rate ↔ %HRR converter
Target Heart Rate Lookup Grid
THR at standard intensities using the Karvonen formula with HRrest = 60 bpm. Values in bpm.
| HRmax | 50% | 60% | 65% | 70% | 75% | 80% | 85% | 90% |
|---|
Training Zone Reference
The five standard heart-rate-reserve zones with bpm bands at your current values and physiological descriptions.
| Zone | % HRR | % HRmax | THR range (bpm) | Physiological description | Typical duration |
|---|
Variable Reference
| Symbol | Meaning | Typical range | Units |
|---|---|---|---|
| THR | Target heart rate | 100 – 190 | bpm |
| HRmax | Maximum heart rate | 150 – 220 | bpm |
| HRrest | Resting heart rate | 40 – 100 | bpm |
| HRR | Heart-rate reserve (HRmax − HRrest) | 60 – 160 | bpm |
| intensity | Fraction of HRR | 0.50 – 1.00 | dimensionless |
| Z1–Z5 | Training zones | 50% – 100% HRR | dimensionless |
| %HRmax | Simple percentage of maximum | 50 – 100 | % |
What Does the Karvonen Formula Measure?
The Karvonen formula gives you a target heart rate for exercise at a chosen intensity. Published by the Finnish physiologist Martti Karvonen in 1957, it was the first method to work from heart-rate reserve — the range between resting and maximum heart rate — rather than from HRmax alone. The insight was simple but profound: two people with the same HRmax but different resting heart rates have different usable ranges, and the same perceived effort occurs at different absolute heart rates. Anchoring the intensity calculation to resting HR personalises every target, which is why Karvonen remains the standard in exercise physiology and clinical cardiology more than sixty years later.
Karvonen Formula
The defining relationship is:
where intensity is expressed as a decimal between 0 and 1. The term (HRmax − HRrest) is the heart-rate reserve (HRR), the difference between the highest and lowest rates your heart can sustain.
Rearranged to solve for the other three unknowns:
HRrest = (THR − intensity·HRmax) / (1 − intensity)
intensity = (THR − HRrest) / (HRmax − HRrest)
For comparison, the simpler %HRmax method uses only HRmax:
The two methods agree exactly when HRrest = 0, and diverge increasingly as HRrest rises. At 70% intensity with HRmax 185 and HRrest 60, Karvonen gives 147.5 bpm while %HRmax gives 129.5 bpm — a difference of 18 bpm.
Karvonen Variables
| Symbol | Meaning | Notes |
|---|---|---|
| THR | Target heart rate | The bpm you aim to maintain during exercise |
| HRmax | Maximum heart rate | Upper anchor; estimate as 220 − age or measure directly |
| HRrest | Resting heart rate | Lower anchor; measured on waking, before rising |
| HRR | Heart-rate reserve | HRmax − HRrest; the usable range |
| intensity | Fraction of reserve | 0.50–0.60 recovery through 0.90–1.00 maximum |
| Z1–Z5 | Training zones | Five bands of 10 percentage points each |
How Each Variable Affects the Target
The Karvonen formula is linear in HRmax and HRrest, with the coefficient on each determined by intensity. Increasing HRmax by 1 bpm raises THR by exactly the intensity fraction — 0.70 bpm at 70%. Increasing HRrest by 1 bpm raises THR by (1 − intensity) — 0.30 bpm at 70%. Decreasing HRrest by the same amount lowers it by the same 0.30 bpm. The intensity coefficient is HRR, so raising intensity by 10 percentage points raises THR by 0.10 × HRR bpm — 12.5 bpm for an HRR of 125.
The practical consequence is that HRmax matters most at high intensity (where its coefficient is close to 1) and HRrest matters most at low intensity (where (1 − intensity) is close to 1). For steady aerobic training at 65–75%, both anchors matter roughly equally. This is why measuring both carefully — rather than relying on age-predicted HRmax alone — is worth the effort for anyone training seriously with heart rate.
Karvonen Calculation Examples
HRR = 185 − 60 = 125 bpm
THR = (125 × 0.70) + 60 = 87.5 + 60 = 147.5 bpm
HRmax = ((147.5 − 60) / 0.70) + 60 = (87.5 / 0.70) + 60 = 125 + 60 = 185 bpm
HRrest = (147.5 − 0.70 × 185) / (1 − 0.70) = (147.5 − 129.5) / 0.30 = 18 / 0.30 = 60 bpm
intensity = (147.5 − 60) / (185 − 60) = 87.5 / 125 = 0.70 (70%)
Karvonen: (125 × 0.70) + 60 = 147.5 bpm
Simple %HRmax: 185 × 0.70 = 129.5 bpm
Difference: 18 bpm — enough to shift the workout by a full zone
Frequently Asked Questions
The simple %HRmax method computes target heart rate as a percentage of HRmax alone — 70% of 185 is 129.5 bpm. The Karvonen method instead works from the reserve between rest and maximum — 70% of (185 − 60) + 60 = 147.5 bpm. The 18 bpm gap reflects the fact that fitter people have lower resting heart rates and therefore wider reserves: at the same perceived effort they reach a higher absolute heart rate. Using %HRmax alone systematically under-prescribes intensity for trained athletes and over-prescribes it for people with high resting heart rates. This is why Karvonen is the standard method in exercise physiology, sports medicine, and clinical cardiac rehabilitation.
Measure it immediately on waking, before getting out of bed, ideally on three consecutive mornings and average the results. Use a chest strap, a finger on the radial artery at the wrist, or a validated wearable. Count beats for a full 60 seconds for best accuracy, or for 30 seconds and double it. Avoid measuring after caffeine, alcohol, illness, or a hard workout the previous day, all of which can raise resting HR by 5–10 bpm. Trained endurance athletes often sit at 40–55 bpm; the general adult range is 60–100 bpm. A resting HR consistently above 100 bpm (tachycardia) warrants a medical review.
Zone 1 (50–60% HRR) is recovery — very easy, used for warm-ups, cool-downs and active recovery between hard sessions. Zone 2 (60–70% HRR) is the aerobic base — the intensity at which fat oxidation peaks and mitochondria adapt most efficiently; most endurance training happens here. Zone 3 (70–80% HRR) is the aerobic sweet spot — moderate effort, sustainable for 30–60 minutes, improves cardiovascular efficiency. Zone 4 (80–90% HRR) is threshold work — the intensity near lactate threshold, hard but sustainable for 15–30 minutes in trained athletes. Zone 5 (90–100% HRR) is maximum — VO₂max intervals, sustainable only for seconds to a few minutes at a time.
Yes — but through resting HR, not through HRmax. Endurance training lowers resting heart rate and increases stroke volume, so the reserve widens. Since Karvonen anchors intensity to the reserve, a lower resting HR shifts every target upward. A 40-year-old whose resting HR falls from 75 to 55 will see their 70% target rise from about 148 bpm to about 162 bpm at the same HRmax of 185. HRmax itself stays essentially fixed with training — it is set by genetics and age — which is why the Karvonen formula is more training-responsive than the %HRmax method. Re-measure resting HR every few months and update the calculator.
A heart-rate monitor shows your live heart rate but does not tell you whether it is in the right zone for the workout you are doing. The Karvonen calculation tells you what the zone boundaries are; the monitor tells you where you are within them. Together they are far more useful than either alone. Most modern wearables and bike computers let you enter zone boundaries manually — compute them once with this calculator and enter them into your device so live training is guided by personal numbers rather than by the device's age-based defaults, which typically use the less accurate %HRmax method.
Beta-blockers blunt heart-rate response to exercise, so heart rate alone under-estimates exercise intensity in patients taking them. The Karvonen formula and %HRmax method both assume a normal heart-rate response, and both are unreliable on beta-blockers. The standard alternative is the RPE (rating of perceived exertion) scale — usually the Borg 6–20 scale — combined with a talk test: if you can hold a conversation, you are in the aerobic zone; if you can only speak in short sentences, you are at threshold. Patients on beta-blockers should have exercise zones set by a cardiologist or exercise physiologist using a supervised test, not by a formula.
Chest straps using electrical signal detection (Polar H10, Garmin HRM-Pro, Wahoo TICKR) are the gold standard for accuracy during exercise, typically within 1–2 bpm of an ECG. Optical wrist sensors have improved dramatically but still lag: they are accurate at steady moderate intensity, but can be 10–20 bpm off during intervals, cold weather, or heavy sweating, and they lock onto cadence during cycling. If you are training by heart rate seriously, a chest strap is worth the investment. Whichever sensor you use, verify it once against a manual pulse count at rest and during a steady moderate effort to catch systematic errors.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| THR | Target heart rate | bpm |
| HRmax | Maximum heart rate | bpm |
| HRrest | Resting heart rate | bpm |
| intensity | Desired intensity (0 to 1) |
What it means
The Karvonen formula calculates target heart rate (THR) for exercise by incorporating resting heart rate (HRrest). It uses the heart rate reserve (HRmax − HRrest) multiplied by desired intensity, then adds HRrest. This accounts for individual fitness and provides a more accurate training zone than a simple percentage of HRmax. It is widely used in cardiopulmonary rehabilitation, athletic training, and fitness programming. For example, an intensity of 60‑80% is common for aerobic conditioning. Understanding this formula helps in prescribing safe and effective exercise loads tailored to an individual’s fitness level.
Worked example
Target Heart Rate (Karvonen) – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| HRmax (bpm) | 180 |
| HRrest (bpm) | 60 |
| intensity | 0.70 |
| Parameter | Value |
|---|---|
| HRmax | 170 |
| HRrest | 70 |
| intensity | 0.60 |
Common mistakes
- Karvonen formula: THR = ((HRmax − HRrest) × intensity) + HRrest – uses heart rate reserve.
- Intensity: Typically 0.5‑0.85 (50‑85% of heart rate reserve).
- HRrest: Resting heart rate – measure when fully rested, preferably in the morning.
- Target zone: Used to prescribe exercise intensity – more accurate than percentage of HRmax alone.
- Medications: Beta‑blockers lower HR – the formula may not apply.
Applications
The Karvonen formula calculates target heart rate (THR) by incorporating the resting heart rate (HRrest) and desired exercise intensity (as a percentage of heart rate reserve). This provides a more personalised and accurate target than simply using a percentage of HRmax. Exercise physiologists, trainers, and cardiac rehabilitation specialists use it to prescribe individualised exercise intensities. By using THR, individuals can optimise cardiovascular benefits while minimising risks. This formula is essential for designing interval training, for tracking fitness improvements (as resting heart rate decreases), and for ensuring that exercise is safe and effective. It is a core tool in clinical and fitness exercise prescription.
- Individualised exercise intensity programming
- Cardiac rehabilitation and post‑infarction exercise
- Fitness assessment and improvement tracking
- Sports training – heart rate zone determination
- Health and wellness coaching
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