QTc formulas compared: Bazett, Fridericia, Framingham and Hodges
Fridericia and Framingham correct the QT for heart rate better than Bazett, which overcorrects at fast rates and undercorrects at slow ones. On the same ECG at 110/min, the four common QTc formulas can differ by more than 50 ms.
At a glance
| Formula | Equation | Type | Fast heart rates | Slow heart rates |
|---|---|---|---|---|
| Bazett (1920) | QT ÷ √RR | Power, exponent 0.5 | Overcorrects: QTc too long | Undercorrects: QTc too short |
| Fridericia (1920) | QT ÷ ∛RR | Power, exponent 0.33 | Much smaller error | Much smaller error |
| Framingham (1992) | QT + 154 × (1 − RR) | Linear | Good | Good |
| Hodges (1983) | QT + 1.75 × (HR − 60) | Linear, uses heart rate | Not directly compared in the sources cited | Can run slightly high |
QT is in milliseconds, RR in seconds (RR = 60 ÷ heart rate) and HR in beats per minute. All four give the same answer at 60 beats per minute, where RR is exactly 1 second.
The formulas fall into two families. Power formulas (Bazett, Fridericia) divide QT by RR raised to an exponent; the larger the exponent, the stronger the correction. Linear formulas (Framingham, Hodges) add or subtract a fixed number of milliseconds for each step away from 60 beats per minute. The real QT–RR relationship differs from person to person, so every population formula is a compromise. Research studies sometimes fit an individual correction for each subject, but that needs many ECGs at different rates and is not practical at the bedside.
Bazett
Bazett divides QT by the square root of RR. It is easy to compute and is still the default on many ECG machines, which is why so many reported QTc values are Bazett values without saying so.
Its weakness is that a square root over-adjusts. As the heart rate rises, RR shrinks and √RR shrinks fast enough to push the QTc up, so a tachycardic patient can look prolonged when the true rate-adjusted QT is normal. At slow rates the opposite happens and a genuinely long QT can be pulled down into the normal range. A large hospital study found that Bazett classified many more patients as prolonged than the other formulas and predicted mortality less well.
Fridericia
Fridericia, published the same year, uses the cube root of RR. The smaller exponent flattens the correction, so the formula stays close to the true rate-independent QT over a wider range of heart rates. The ICH E14 guideline describes it as more accurate than Bazett at altered heart rates, and it is the usual primary formula in regulatory QT studies. The QTc calculator on this site uses Fridericia as its default for the same reason.
Framingham
The Framingham formula comes from linear regression on about 5,000 people in the Framingham Heart Study. It adds 154 ms for every second the RR interval is shorter than 1 (and subtracts when it is longer). In the Leuven study by Vandenberk and colleagues, Framingham and Fridericia gave the best rate correction and the best prediction of 30-day and 1-year mortality.
Hodges
Hodges is also linear but works directly with heart rate: 1.75 ms is added for each beat per minute above 60. Because it does not need the RR interval, it is handy at the bedside. At slow rates it tends to give slightly higher values than Fridericia or Framingham.
Same patient, different answers
Example 1: fast rate. QT 360 ms, heart rate 110/min, so RR = 60 ÷ 110 = 0.545 s.
| Formula | QTc |
|---|---|
| Bazett | 487 ms |
| Fridericia | 441 ms |
| Framingham | 430 ms |
| Hodges | 448 ms |
Bazett is above both the 450 ms (men) and 460 ms (women) thresholds; the other three are below both. The 57 ms gap between Bazett and Framingham comes entirely from the choice of formula.
Example 2: slow rate. QT 460 ms, heart rate 50/min, so RR = 1.2 s.
| Formula | QTc |
|---|---|
| Bazett | 420 ms |
| Fridericia | 433 ms |
| Framingham | 429 ms |
| Hodges | 443 ms |
Now Bazett gives the lowest value. At slow rates its undercorrection can hide a long QT rather than create one.
These are the values the QTc calculator shows when you enter the same QT and heart rate; it lists all four formulas side by side.
Which QTc formula should you use?
- Regulatory studies. ICH E14 asks for uncorrected QT and RR together with Bazett- and Fridericia-corrected values in every submission, and states that Bazett overcorrects at high rates and undercorrects below 60 beats per minute. Thresholds of interest include QTc above 450, 480 and 500 ms and increases from baseline of more than 30 and 60 ms.
- Professional recommendations. The AHA/ACCF/HRS 2009 statement recommends a linear regression formula rather than Bazett, and defines prolonged QTc as 450 ms or more in men and 460 ms or more in women, with 390 ms or less as short.
- Monitoring on the ward. Fridericia or Framingham are the most defensible general choices, particularly when the heart rate is outside about 50–100/min. Whatever formula is used, using the same one each time keeps serial readings comparable. Normal heart rate ranges are in the guide to normal vital signs by age.
Thresholds and actions differ between institutions and drug labels, so we recommend checking the protocol and product information you work with.
Common pitfalls
- Trusting the machine QTc blindly. Automated measurements are often Bazett and can misplace the end of the T wave. Many protocols ask for a manual check of the QT.
- Switching formulas between ECGs, which creates an apparent change that is only arithmetic.
- Correcting at extreme rates. Above roughly 100–120/min or below 50/min every formula becomes less reliable; repeating the ECG at a steadier rate is often more informative than any correction.
- Including U waves or measuring in a lead with a flat T wave, which lengthens the QT artificially. Lead II or V5 is commonly used.
- Wide QRS. Bundle branch block or ventricular pacing lengthens the QT through depolarisation rather than repolarisation; specialist methods (such as the JT interval) are used instead.
- Atrial fibrillation. A single beat-to-beat RR is misleading; averaging over several beats is usual.
- Forgetting units. RR must be in seconds for Bazett, Fridericia and Framingham; using milliseconds gives nonsense.
- QT: from the start of the QRS complex to the end of the T wave, usually in lead II or V5.
- RR: the distance between two R waves. The calculator works it out from the heart rate (RR = 60 ÷ rate).
The end of the T wave is often found with the tangent method; a U wave is generally not included.
Frequently asked questions
Why does the QT interval need correcting?
Because ventricular repolarisation is quicker at faster heart rates, so the raw QT shortens as the rate rises. Correction rescales it to what it would be at 60 beats per minute. That lets you compare readings taken at different rates, and compare them with one threshold such as 450 or 460 ms.
Why is Bazett still printed on most ECGs?
Because it is the oldest and simplest formula, and it became the default in many ECG machines and textbooks. It works reasonably well around 60–70 beats per minute but overcorrects at fast rates and undercorrects at slow ones. At 110/min it can read 57 ms higher than Framingham.
Which QTc formula does the FDA use?
Both Bazett and Fridericia, with Fridericia usually the main one. The ICH E14 guideline, followed by the FDA and EMA, asks drug developers to submit QT corrected with both formulas and notes that Fridericia is more accurate at altered heart rates. ICH E14 notes that Bazett and Fridericia are the most widely used corrections.
What QTc is considered prolonged?
The AHA/ACCF/HRS recommendations use 450 ms or more in men and 460 ms or more in women. A QTc above 500 ms, or a rise of more than 60 ms from baseline, is widely treated as a marker of markedly increased risk of torsades de pointes.
Do all four formulas agree at 60 beats per minute?
Yes. At 60 beats per minute the RR interval is exactly 1 second, and every formula returns the measured QT unchanged. The differences appear only as the rate moves away from 60, and they grow the further it moves: at 110/min, the four results in the worked example span 57 ms.
Can QTc be calculated in atrial fibrillation?
Yes, but with more uncertainty, because each beat has a different RR interval and a single beat-to-beat RR is misleading. A common approach is to average QT and RR over several beats and then correct the averages. The same formula should be used each time, so serial ECGs stay comparable.
Sources
- Bazett HC. An analysis of the time-relations of electrocardiograms. Heart 1920;7:353–370
- Fridericia LS. The duration of systole in an electrocardiogram in normal humans and in patients with heart disease (1920, English translation). Ann Noninvasive Electrocardiol 2003;8:343–351
- Hodges M, Salerno D, Erlien D. Bazett’s QT correction reviewed: evidence that a linear QT correction for heart rate is better. J Am Coll Cardiol 1983;1:694 (abstract)
- Vandenberk B, et al. Which QT correction formulae to use for QT monitoring? J Am Heart Assoc 2016
- Rautaharju PM, et al. AHA/ACCF/HRS recommendations for the standardization and interpretation of the electrocardiogram, part IV: the ST segment, T and U waves, and the QT interval. Circulation 2009
- ICH E14. The clinical evaluation of QT/QTc interval prolongation and proarrhythmic potential for non-antiarrhythmic drugs
- Sagie A, et al. An improved method for adjusting the QT interval for heart rate (the Framingham Heart Study). Am J Cardiol 1992