Penn State Equation Calculator (Ventilated)
Penn State Equation Calculator (Ventilated Patients)
The equation the Academy of Nutrition and Dietetics recommends for mechanically ventilated adults when indirect calorimetry is unavailable — PSU(2003b), and the PSU(2010) modification for patients 60 and over with a BMI of 30 or more.
Penn State resting metabolic rate
Mifflin, Tmax and minute ventilationPSU(2003b). Male, 70 kg, 176 cm, 45 years; Tmax 38.5 °C; minute ventilation 10.0 L/min
Both versions
RMR = Mifflin-St Jeor × 0.96 + Tmax × 167 + V̇E × 31 − 6212
PSU(2010), modified
RMR = Mifflin-St Jeor × 0.71 + Tmax × 85 + V̇E × 64 − 3085
- Mifflin-St Jeor
- the same equation as the Mifflin-St Jeor calculator, computed from sex, weight, height and age and then scaled. Both versions wrap it rather than replacing it, so the 166 kcal/day sex intercept propagates through, scaled by 0.96 or 0.71
- Tmax and V̇E
- Tmax is the HIGHEST body temperature of the preceding 24 hours in degrees Celsius, not the current one; V̇E is expired minute ventilation in L/min off the ventilator. Tmax is worth 167 kcal/day per degree in PSU(2003b) and 85 in PSU(2010); V̇E is worth 31 per L/min and then 64. The two terms nearly swap importance between versions, so transposing them is a real error rather than a rounding
- which version, by population
- PSU(2003b) in non-obese ventilated adults (69% accurate under 60, 77% at 60 and over) and in ventilated adults with obesity under 60 (70%); PSU(2010) at 60 or over with a BMI of 30 or more (74%, against 58% for the original). Both Academy recommendations are rated Fair, Conditional
- ventilated patients only
- the minute-ventilation term cannot be read in a spontaneously breathing patient. A modification with that term removed was tested in 55 acutely ill non-ventilated patients and was accurate in 71%, but only above a BMI of 20.5 kg/m²; that is a different equation and is not implemented here
Worked example
PSU(2003b). Male, 70 kg, 176 cm, 45 years; Tmax 38.5 °C; minute ventilation 10.0 L/min
Mifflin-St Jeor first: 10 × 70 + 6.25 × 176 − 5 × 45 + 5 = 1,580 kcal/day
× 0.96 = 1,516.8; + 38.5 × 167 = + 6,429.5; + 10.0 × 31 = + 310.0; − 6,212
1,516.8 + 6,429.5 + 310.0 − 6,212 = 2,044.3 kcal/day, rounded to 2,044
That is 29.2 kcal/kg/day and 464.3 kcal/day above bare Mifflin-St Jeor — the fever and the minute ventilation are doing that work, which is why a resting equation alone understates a ventilated patient
PSU(2010) on the same inputs returns 1,949.3, 95 kcal/day lower. The page shows both and flags a version used outside its recommended population
Swap Tmax and minute ventilation — 10.0 °C and 38.5 L/min — and PSU(2003b) returns −1,831.7, obviously wrong. In PSU(2010), where the coefficients are 85 and 64 rather than 167 and 31, the same transposition gives 1,350.8: a plausible-looking wrong answer 598.5 kcal/day low
Which version, in which patient, and how accurate
| Population | Academy recommendation | Accuracy rate | Rating |
|---|---|---|---|
| Ventilated, non-obese, under 60 | PSU(2003b) | 69% | Fair, Conditional |
| Ventilated, non-obese, 60 and over | PSU(2003b) | 77% | Fair, Conditional |
| Ventilated, BMI 30 or more, under 60 | PSU(2003b) | 70% | Fair, Conditional |
| Ventilated, BMI 30 or more, 60 and over | PSU(2010) | 74% (against 58% for PSU(2003b)) | Fair, Conditional |
| Acutely ill, NOT ventilated | Neither — the ventilation term cannot be read | A variant without that term was accurate in 71% of 55 patients, and only above a BMI of 20.5 | Not implemented here |
How the two versions weight their three terms
| Term | PSU(2003b) | PSU(2010) | Value at the worked example |
|---|---|---|---|
| Mifflin-St Jeor | × 0.96 | × 0.71 | 1,516.8 against 1,121.8 |
| Tmax, per °C | × 167 | × 85 | 6,429.5 against 3,272.5 |
| Minute ventilation, per L/min | × 31 | × 64 | 310.0 against 640.0 |
| Constant | − 6,212 | − 3,085 | — |
| Result | — | — | 2,044.3 against 1,949.3 |
Why a ventilated patient needs its own equation
Resting metabolic rate in a ventilated critical care patient is not well predicted by equations built on healthy volunteers. Fever, the inflammatory response and the work of breathing all raise expenditure, and none of them appears in sex, weight, height and age. The Penn State equations add the two bedside variables that carry that information — the highest temperature of the preceding 24 hours and the minute ventilation on the ventilator — and scale a Mifflin-St Jeor figure with them.
The validation is unusually explicit. In 47 ventilated surgical, trauma and medical patients the Penn State equations were accurate in 72% at best against 60% for Ireton-Jones, with errors above 15% in 11% against 32%. In 202 ventilated patients, accuracy across eleven methods ran from 67% for Penn State down to 18% for the weight-adjusted Harris-Benedict equation, with one subgroup at 0%; Penn State was the only equation unbiased and precise across all four age and obesity subgroups. The group it struggled with was patients 60 or over with a BMI of 30 or more, so a separate regression was computed for them and later validated: 74% accurate against 58% for the original. That is why there are two versions, and why this page asks for height as well as weight.
Two inputs are routinely mis-entered. Tmax is the maximum temperature over 24 hours, not the reading now; at 167 kcal/day per degree in PSU(2003b), using the current temperature in a patient whose fever has broken costs several hundred kcal/day. And minute ventilation is the expired minute volume in L/min, not tidal volume and not respiratory rate. Those two terms are not interchangeable either: their coefficients swap importance between versions, 167 and 31 becoming 85 and 64, so a transposition in PSU(2010) produces a wrong answer that looks entirely plausible.
The honest framing is ESPEN’s. Energy expenditure should be determined by indirect calorimetry in ventilated patients — recommendation 15, Grade B — and predictive equations are “associated with significant inaccuracy (up to 60%)”. Penn State is what to use when the metabolic cart is not there; see the Weir equation calculator for what the cart computes and the respiratory quotient calculator for the ratio reported with it. ESPEN also caps the early phase at 70% of expenditure however obtained, rising to 80 to 100% of the measured figure after day 3. This page computes a figure and prints the published targets beside it with the guideline each comes from. The prescription is the clinician’s, taken with the patient in front of them.
Frequently asked questions
What is the Penn State equation?
A predictive equation for resting metabolic rate in mechanically ventilated critical care patients. PSU(2003b) is Mifflin-St Jeor × 0.96 + Tmax × 167 + minute ventilation × 31 − 6212, where Tmax is the highest temperature of the last 24 hours in degrees Celsius and minute ventilation is in L/min.
Which Penn State equation should I use?
The Academy of Nutrition and Dietetics recommends PSU(2003b) for non-obese ventilated adults at any age and for ventilated adults with obesity under 60; and PSU(2010) — Mifflin × 0.71 + Tmax × 85 + minute ventilation × 64 − 3085 — at 60 or over with a BMI of 30 kg/m² or more. This page flags a version used outside its recommended population.
How accurate is the Penn State equation?
Published accuracy rates — patients predicted within 10% of measured — are 69% in non-obese ventilated adults under 60, 77% at 60 and over, 70% in those with obesity under 60, and 74% for PSU(2010) at 60 or over with obesity. Across 202 ventilated patients the overall rate was 67%, the best of eleven methods tested. ESPEN still recommends indirect calorimetry where it is available.
Can I use Penn State in a patient who is not on a ventilator?
No, because the minute-ventilation term cannot be read. A variant with that term removed was accurate in 71% of 55 acutely ill spontaneously breathing patients, but only above a BMI of 20.5 kg/m²; that is a separate equation and is not implemented here. For a non-ventilated adult, Mifflin-St Jeor is better validated.
Is Tmax the current temperature?
No — it is the highest body temperature recorded in the preceding 24 hours, and this is the commonest way the equation is mis-entered. In PSU(2003b) every degree is worth 167 kcal/day, so entering a normal current temperature in a patient who spiked to 39 °C overnight understates expenditure by several hundred kcal/day.
Related calculators
References
- Frankenfield D, Smith JS, Cooney RN. Validation of 2 approaches to predicting resting metabolic rate in critically ill patients. JPEN J Parenter Enteral Nutr. 2004;28(4):259–264. 47 ventilated patients: Penn State accurate in 72% at best against 60% for Ireton-Jones, with errors above 15% in 11% against 32%.
- Frankenfield DC, et al. Analysis of estimation methods for resting metabolic rate in critically ill adults. JPEN J Parenter Enteral Nutr. 2009;33(1):27–36. 202 ventilated patients; accuracy 67% for Penn State down to 18% for the weight-adjusted Harris-Benedict equation. Source of the modified regression, Mifflin(0.71) + Tmax(85) + Ve(64) − 3085.
- Frankenfield DC. Validation of an equation for resting metabolic rate in older obese, critically ill patients. JPEN J Parenter Enteral Nutr. 2011;35(2):264–269. Accuracy 74% for the modified Penn State equation against 58% for the original, in patients aged 60 or over with a BMI of 30 kg/m² or more.
- Academy of Nutrition and Dietetics Evidence Analysis Library. Critical Illness: best method to estimate RMR (2010). PSU(2003b) in non-obese ventilated adults, 69% accurate under 60 years and 77% at 60 and over, and in ventilated adults with obesity under 60, 70%; PSU(2010) at 60 and over with obesity, 74%. Both Fair, Conditional.
- Frankenfield DC, Ashcraft CM. Toward the development of predictive equations for resting metabolic rate in acutely ill spontaneously breathing patients. JPEN J Parenter Enteral Nutr. 2017;41(7):1155–1161. A Penn State variant with the ventilation term removed was accurate in 71% of 55 non-ventilated patients, and only above a BMI of 20.5 kg/m².
- Singer P, Blaser AR, Berger MM, et al. ESPEN guideline on clinical nutrition in the intensive care unit. Clin Nutr. 2019;38(1):48–79. Recommendations 15 (indirect calorimetry in ventilated patients, Grade B), 17 (not exceeding 70% of energy expenditure in the early phase), 22 (1.3 g/kg protein equivalents), 23 (glucose “should not exceed 5 mg/kg/min”) and 25 (lipids “should not exceed 1.5 g lipids/kg/day”). Predictive equations are “associated with significant inaccuracy (up to 60%)”, with 20–25 kcal/kg/day named as the simplest alternative.
Not medical advice. For healthcare professionals and education. Reference intervals vary by laboratory and assay — always use your own laboratory's. Never base a dose or a treatment decision on this page alone. Full disclaimer at calcengines.com/disclaimer/