QTc formulas compared: Bazett vs Fridericia vs Framingham vs Hodges

A QT of 320 ms at 120 bpm corrects to 452.5 ms by Bazett, 403.2 by Fridericia, 397.0 by Framingham and 425.0 by Hodges, a 55.5 ms spread. Only Bazett reaches 450 ms, where an adult man’s QTc counts as prolonged, and Bazett over-corrects at fast rates. At 60 bpm all four return the measured QT unchanged.

Line chart of QTc against heart rate from 40 to 150 bpm for a measured QT of 360 ms. Bazett, a solid line with circles, rises from 293.9 ms to 569.2 ms, the steepest. Fridericia, a dashed line with squares, rises from 314.5 to 488.6. Framingham, a dotted line with triangles, rises from 283.0 to 452.4, the flattest. Hodges, a dash-dot line with diamonds, rises from 325.0 to 517.5. All four cross at 360 ms at 60 bpm. Dashed reference lines mark 450 ms for men and 460 ms for women. Framingham was fitted only at 41 to 120 bpm and Hodges tested only under 90 bpm. — QTc by the four formulas for a measured QT of 360 ms, 40 to 150 bpm, with the AHA/ACCF/HRS limits for a prolonged QTc in adults (Rautaharju 2009). Framingham was fitted at 41 to 120 bpm and Hodges tested under 90 bpm; the table marks the points outside. Every plotted point is a row of the table. Image © ScienceQuest, CC BY 4.0: free to reuse with credit and a link to this page, as the image licence explains.

QTc by heart rate, measured QT 360 ms

QTc by Bazett, Fridericia, Framingham and Hodges for a measured QT of 360 ms at heart rates from 40 to 150 bpm, with the RR interval and the spread between the four
Heart rate (bpm)	RR s	Bazett ms	Fridericia ms	Framingham ms	Hodges ms	Spread ms
40	1.500	293.9	314.5	283.0†	325.0	42.0†
50	1.200	328.6	338.8	329.2	342.5	13.9
60	1.000	360.0	360.0	360.0	360.0	0.0
70	0.857	388.8	379.0	382.0	377.5	11.3
80	0.750	415.7	396.2	398.5	395.0	20.7
90	0.667	440.9	412.1	411.3	412.5	29.6
100	0.600	464.8	426.8	421.6	430.0†	43.2
110	0.545	487.4	440.6	430.0	447.5†	57.4
120	0.500	509.1	453.6	437.0	465.0†	72.1
130	0.462	529.9	465.8	442.9†	482.5†	87.0†
140	0.429	549.9	477.5	448.0†	500.0†	101.9†
150	0.400	569.2	488.6	452.4†	517.5†	116.8†

RR = 60 ÷ heart rate. The spread is the highest QTc minus the lowest, worked before rounding, and is marked when either end is. † Outside the range the formula was fitted or tested over: Framingham’s 41 to 120 bpm (Sagie 1992) and Hodges’s under 90 bpm (Vandenberk 2016).

Six example tracings

QTc by the four formulas for six pairs of heart rate and measured QT, from 50 to 140 bpm, with the formulas whose QTc reaches 450 ms, the AHA/ACCF/HRS limit for adult men (Rautaharju 2009)
Tracing	Bazett ms	Fridericia ms	Framingham ms	Hodges ms	Spread ms	450 ms or more
50 bpm, 440 ms	401.7	414.1	409.2	422.5	20.8	None
60 bpm, 400 ms	400.0	400.0	400.0	400.0	0.0	None
80 bpm, 380 ms	438.8	418.2	418.5	415.0	23.8	None
100 bpm, 340 ms	438.9	403.1	401.6	410.0†	37.3	None
120 bpm, 320 ms	452.5	403.2	397.0	425.0†	55.5	Bazett
140 bpm, 290 ms	443.0	384.6	378.0†	430.0†	65.0†	None

The last column tests 450 ms on unrounded values. For a woman the limit is 460 ms, which none of these six reaches by any formula. † Outside the range the formula was fitted or tested over: Framingham’s 41 to 120 bpm (Sagie 1992) and Hodges’s under 90 bpm (Vandenberk 2016).

The measured QT that reaches the limit

The shortest measured QT, in whole ms, at which each formula gives a QTc of 450 ms (men) or 460 ms (women), the AHA/ACCF/HRS limits for adults (Rautaharju 2009), at heart rates from 50 to 130 bpm
Formula, sex	Heart rate (bpm)
Formula, sex	50	60	70	80	90	100	110	120	130
Bazett, men	493	450	417	390	368	349	333	319	306
Fridericia, men	479	450	428	409	394	380	368	358	348
Framingham, men	481	450	428	412	399	389	380	373	368†
Hodges, men	468	450	433	415	398	380†	363†	345†	328†
Bazett, women	504	460	426	399	376	357	340	326	313
Fridericia, women	489	460	437	418	402	388	376	366	356
Framingham, women	491	460	438	422	409	399	390	383	378†
Hodges, women	478	460	443	425	408	390†	373†	355†	338†

The shortest measured QT, in whole ms, that reaches the limit by that formula, found by bisection on the formula itself. † Outside the range the formula was fitted or tested over: Framingham’s 41 to 120 bpm (Sagie 1992) and Hodges’s under 90 bpm (Vandenberk 2016).

Why the formulas disagree

Each formula estimates the QT the same heart would show at 60 bpm, where RR is exactly 1 second, so all four return the measured QT at that rate. Away from 60 they part. Bazett divides by the square root of RR and Fridericia by the cube root, and for an RR under 1 second the square root is the smaller divisor. So above 60 bpm Bazett gives the higher QTc, 509.1 ms against Fridericia’s 453.6 for a QT of 360 ms at 120 bpm, and below 60 the order reverses.

Bazett fitted his curve to 39 young subjects in 1920. In 1992 Sagie and colleagues fitted a straight line to 5,018 Framingham adults aged 28 to 62, at rates from 41 to 120 bpm, and found that Bazett over-corrects at fast rates and under-corrects at slow ones. Hodges’s line adds 1.75 ms for each beat per minute above 60. Vandenberk’s group ran these four, and Rautaharju’s, on one ECG from each of 6,609 adults at University Hospitals Leuven, in sinus rhythm under 90 bpm with a QRS of 120 ms or less: Fridericia and Framingham removed the effect of rate best, and Bazett did worst.

At 120 bpm a man’s QTc reaches 450 ms by Bazett from a measured QT of 319 ms, and by Framingham only from 373 ms. In Vandenberk’s healthy subset, Bazett’s 99th-percentile QTc was 472 ms in men and 482 ms in women, above the 450 and 460 ms limits. ICH E14 (2005) asks drug applications for the raw QT, RR and rate beside both Bazett and Fridericia, because “the best correction approach is a subject of controversy”.

The formulas

Bazett [1]: $\mathrm{QTc} = \dfrac{\mathrm{QT}}{\sqrt{\mathrm{RR}}}$
Fridericia [2]: $\mathrm{QTc} = \dfrac{\mathrm{QT}}{\sqrt[3]{\mathrm{RR}}}$
Framingham [3]: $\mathrm{QTc} = \mathrm{QT} + 154 \times (1 - \mathrm{RR})$
Hodges [4]: $\mathrm{QTc} = \mathrm{QT} + 1.75 \times (\mathrm{HR} - 60)$

Where each formula holds

Each formula’s sample, the people it holds for, and where it does not apply
Formula	Fitted in	Holds for	Not for
Bazett (1920)	39 young subjects	Rates near 60 bpm, and comparison with the many clinical reports that use it (ICH E14 3.1.1)	Fast rates, where it over-corrects (452.5 ms for 320 ms at 120 bpm), and slow rates, where it under-corrects. Rautaharju 2009 recommends linear regression corrections over Bazett, which can flag a normal QT as prolonged
Fridericia (1920)	Normal subjects and patients with heart disease	Drug trials, where ICH E14 asks for it beside Bazett; more accurate than Bazett at fast and slow rates	Removing rate entirely: it leaves a negative correlation with rate (r of −0.26 to −0.32)
Framingham (Sagie 1992)	5,018 adults aged 28 to 62 without coronary disease, at 41 to 120 bpm	Adults in sinus rhythm at 41 to 120 bpm, the range it was fitted over	Rates outside 41 to 120 bpm, or children
Hodges (1983)	Not reported: the 1983 conference abstract is not online	Sinus rhythm under 90 bpm, where Vandenberk found it within 1 ms of Fridericia on average	Rates above 90 bpm, which Vandenberk’s comparison left out
All four	Sinus rhythm ECGs	One steady rate, with a measurable end of the T wave	Atrial fibrillation, where RR varies beat to beat, or a wide QRS (bundle branch block or a paced rhythm), which lengthens the QT

Calculators and simulators

A study tool, not a clinical one

This page exists for understanding why the QT interval has to be corrected for rate at all, and how much of a reported QTc is the formula rather than the measurement. It is not clinical decision support and must not be used to treat anybody.

A row in these tables is not your patient. Each row fixes the other inputs at the values its caption gives, and a real patient differs in all of them at once, so work a patient’s own figures in the calculator.
Check the units before you trust a number. American and Indian reports mostly use mg/dL, while British, Canadian and Australian reports use mmol/L or µmol/L, and a unit mismatch is the most common way an otherwise correct formula produces a dangerous answer.

Three more cautions

Each formula has a population. The table of where each one holds gives the people each was fitted in, and each is least reliable outside them.
Know which equation your course or laboratory uses. The ones compared here give different numbers for the same patient, which is what the tables show.
Every cell is worked by the calculators’ own code. If a figure does not match what you were taught, check it against the formulas above, and tell us if we have it wrong. How the tools are checked is set out in the editorial policy.

Sources

Bazett HC. An analysis of the time-relations of electrocardiograms. Heart 1920;7:353 to 370. Reprinted in Annals of Noninvasive Electrocardiology 1997;2(2):177 to 194. doi:10.1111/j.1542-474X.1997.tb00325.x
Fridericia LS. Die Systolendauer im Elektrokardiogramm bei normalen Menschen und bei Herzkranken. Acta Medica Scandinavica 1920;53:469 to 486. Translated by Gisela Beutner as The duration of systole in an electrocardiogram in normal humans and in patients with heart disease, Annals of Noninvasive Electrocardiology 2003;8(4):343 to 351. doi:10.1046/j.1542-474X.2003.08413.x
Sagie A, Larson MG, Goldberg RJ, Bengtson JR, Levy D. An improved method for adjusting the QT interval for heart rate (the Framingham Heart Study). American Journal of Cardiology 1992;70(7):797 to 801. doi:10.1016/0002-9149(92)90562-D
Hodges M, Salerno D, Erlien D. Bazett’s QT correction reviewed: evidence that a linear QT correction for heart rate is better. Journal of the American College of Cardiology 1983;1:694. A conference abstract with no full paper online; the link is Vandenberk 2016, which writes the formula out and cites it. Corrected in J Am Heart Assoc 2018;7:e004252 (the Hodges formula). https://doi.org/10.1161/JAHA.116.003264
Vandenberk B, Vandael E, Robyns T, Vandenberghe J, Garweg C, Foulon V, Ector J, Willems R. Which QT correction formulae to use for QT monitoring? Journal of the American Heart Association 2016;5(6):e003264. Corrected in J Am Heart Assoc 2018;7:e004252 (the Hodges formula). doi:10.1161/JAHA.116.003264
Correction to Vandenberk et al., Which QT correction formulae to use for QT monitoring? Journal of the American Heart Association 2018;7(16):e004252. It gives Hodges’s formula as QTc = QT + 1.75 × (60/RR − 60). doi:10.1161/JAHA.117.004252
Rautaharju PM, Surawicz B, Gettes LS, 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;119(10):e241 to e250. doi:10.1161/CIRCULATIONAHA.108.191096
ICH E14. The clinical evaluation of QT/QTc interval prolongation and proarrhythmic potential for non-antiarrhythmic drugs. Step 4 version, 12 May 2005, section 3.1 (3.1.1, population-derived correction formulae). https://database.ich.org/sites/default/files/E14_Guideline.pdf