Health

Calculate the heart-rate–corrected QT interval (QTc) with three formulae. Bazett (1920): QTc = QT/√RR (classic; over-corrects at high HR, under-corrects at low HR). Fridericia (1920): QTc = QT/RR^(1/3) — more accurate across a wide HR range, preferred for drug/QT studies. Framingham (1992): QTc = QT + 0.154×(1 − RR) — simple linear regression. RR is derived from heart rate (RR = 60/HR) when not provided; QT and QTc in ms. Thresholds: men > 450 ms borderline / > 480 ms prolonged; women > 460 ms borderline / > 480 ms prolonged; > 500 ms markedly prolonged. Derived from Bazett 1920, Fridericia 1920, Sagie/Framingham 1992, AHA 2009, ICH E14, and MDCalc. Not medical advice.

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Calculate the serum Anion Gap (AG) to classify metabolic acidosis. Standard formula AG = Na⁺ − Cl⁻ − HCO₃⁻ (mmol/L), or AG = Na⁺ + K⁺ − Cl⁻ − HCO₃⁻ with optional potassium. A high AG (≈ >12, or >20 with K⁺) indicates accumulation of unmeasured anions (lactic acidosis, ketoacidosis, renal failure, and toxins such as methanol/ethylene glycol, salicylates — mnemonic GOLD-MARK). A normal AG (8–12) during metabolic acidosis points to a hyperchloremic (normal-anion-gap) acidosis: diarrhea, renal tubular acidosis, saline resuscitation. A low AG (<3–6) is usually hypoalbuminemia, also hypercalcemia/hypermagnesemia, lithium, cationic IgG paraproteins, or bromide pseudo-hyperchloraemia. Optional albumin correction AG_corrected = AG + 2.5 × (4.0 − albumin g/dL) avoids missing a high-AG acidosis in hypoalbuminemia. Derived from Kraut CJASN 2007, Figge 1998, and MDCalc. Interpret with blood gas and full clinical context. Not medical advice.

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Parse & validate FEN board snapshots, PGN/SAN movetext (with parity, check/mate counts, threefold); compute Elo rating updates from win/draw/loss results, with Lichess/Chess.com tier bands

Health

Calculate the albumin-corrected total calcium to avoid missing true hypocalcemia or hypercalcemia in hypoalbuminemia. Conventional formula (calcium mg/dL, albumin g/dL): Ca_corr = Ca + 0.8 × (4.0 − Albumin). SI formula (calcium mmol/L, albumin g/L): Ca_corr = Ca + 0.02 × (40 − Albumin). Roughly 40% of circulating calcium is albumin-bound, so low albumin lowers the measured total without changing the physiologically active ionized fraction. Corrected reference range ≈ 8.5–10.5 mg/dL (2.15–2.60 mmol/L). Low → true hypocalcemia (hypoparathyroidism, vitamin-D deficiency, CKD, hypomagnesemia, citrated transfusion, pancreatitis, sepsis); high → true hypercalcemia (primary hyperparathyroidism, malignancy/PTHrP, myeloma, vitamin-D intoxication, thiazides, immobilization, granulomatous disease). When albumin is markedly abnormal or acid-base is deranged, ionized calcium remains the gold standard. Based on Payne BMJ 1973 and MDCalc. Not medical advice.

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Calculate the glucose-corrected serum sodium to reveal true body tonicity in hyperglycemia. Classic Katz (1973) formula Na_corr = Na + 1.6 × (Glucose − 100)/100 (glucose mg/dL), or Hillier (1999) Na_corr = Na + 2.4 × (Glucose − 100)/100 which is more accurate at very high glucose (Katz tends to underestimate). Glucose unit selectable: mg/dL or mmol/L (reference 5.5 mmol/L). Hyperglycemia shifts water extracellularly and dilutes sodium; the corrected value reflects the real water balance. Corrected Na < 135 indicates true hyponatremia (DKA/HHS with free-water excess, SIADH, GI/renal losses); > 145 indicates true hypernatremia (common in HHS, signals free-water deficit and guides replacement). Derived from Katz NEJM 1973, Hillier 1999, Adrogué NEJM 2000, and MDCalc. Not medical advice.

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Calculate the Apgar score to assess newborn condition at 1 minute and 5 minutes after birth. Five signs are each scored 0–2 at both time points: Appearance (skin color), Pulse (heart rate), Grimace (reflex irritability), Activity (muscle tone), and Respiration. Each time point totals 0–10. Interpretation: 7–10 reassuring; 4–6 moderately abnormal (may need assistance); 0–3 critically low (immediate resuscitation). The tool reports both the 1-min and 5-min scores, the change (delta), and per-time-point interpretation. A 5-min score, and especially the change from 1 to 5 min, indicates response to resuscitation; persistent low 5-min scores warrant continued resuscitation and reassessment at 10 min. Derived from Apgar 1953, reaffirmed by ACOG/AAP. The Apgar is a physiologic snapshot at a moment in time and is not, by itself, a marker of asphyxia or long-term neurologic outcome. Not medical advice.

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Calculate the 2005 Caprini Risk Assessment Model to stratify venous thromboembolism (VTE) risk in surgical patients. ~40 items weighted 1/2/3/5 points: 1 point (age 41-60, minor surgery, BMI >25, swollen legs, varicose veins, pregnancy/postpartum, recurrent miscarriage, OCP/HRT, sepsis <1mo, lung disease/pneumonia <1mo, COPD, acute MI, CHF <1mo, bedridden, medical bed rest, IBD); 2 points (age 61-74, arthroscopic surgery, major open surgery >45min, laparoscopic >45min, malignancy, bed >72h, plaster cast, central line); 3 points (age ≥75, personal/family VTE history, factor V Leiden, prothrombin 20210A, lupus anticoagulant, anticardiolipin, homocysteine, HIT, other thrombophilia); 5 points (stroke <1mo, elective major lower-extremity arthroplasty, hip/pelvis/leg fracture <1mo, acute spinal cord injury <1mo, multiple trauma <1mo). Management tiers: 0 lowest, 1-4 low-moderate (mechanical), 5-6 high (consider LMWH 7-10d), 7-8 high (LMWH 7-10d), ≥9 highest (LMWH 30d). Derived from Caprini 2005. Not medical advice.

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Calculate the Charlson Comorbidity Index (CCI), including the age-adjusted variant, to predict 1-year mortality from chronic comorbidities. 19 comorbidities are weighted by mortality risk: 1 point (MI, CHF, PVD, cerebrovascular disease, dementia, chronic pulmonary disease, connective tissue disease, peptic ulcer, mild liver disease, diabetes without complications); 2 points (hemiplegia/paraplegia, moderate-to-severe CKD, diabetes with end-organ damage, any non-metastatic tumor, leukemia, lymphoma); 3 points (moderate-to-severe liver disease); 6 points (metastatic solid tumor, AIDS). Age adjustment adds 1 point per decade ≥50 (50-59 +1 … ≥90 +5). Interpretation: 0 ~8%, 1-2 ~25%, 3-4 ~50%, ≥5 ~80-90% 1-year mortality (derivation cohort). Derived from Charlson 1987 (J Chronic Dis) and the 1994 validation. Not medical advice.

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Calculate the Child-Pugh score to grade chronic liver disease / cirrhosis severity and estimate perioperative mortality. Five parameters scored 1–3 each (total 5–15): Total bilirubin (<2 mg/dL =1, 2–3 =2, >3 =3) — supports mg/dL or µmol/L input (auto ÷17.1); Serum albumin (>3.5 g/dL =1, 2.8–3.5 =2, <2.8 =3); INR (<1.7 =1, 1.7–2.3 =2, >2.3 =3); Ascites (absent =1, slight/controlled =2, moderate–severe =3); Hepatic encephalopathy (none =1, grade I–II =2, grade III–IV =3). Classes: A (5–6) well-compensated (1-y ~100%, 2-y ~85%); B (7–9) significant compromise (1-y ~80%, 2-y ~60%); C (10–15) decompensated (1-y ~45%, 2-y ~35%). Derived from Pugh et al. 1973 (Br J Surg) and the original Child-Turcotte classification. Not medical advice.

Health

Calculate the Urine Anion Gap (UAG) to differentiate causes of normal-anion-gap (hyperchloremic) metabolic acidosis: UAG = (U_Na + U_K) − U_Cl, in mmol/L. The UAG is an inverse surrogate for urinary NH₄⁺ excretion. A negative UAG (typically −20 to −50) indicates appropriate high NH₄⁺ excretion → extrarenal (GI) bicarbonate loss (diarrhea, fistulae, ureteral diversions). A positive/high UAG indicates low NH₄⁺ excretion → renal tubular acidosis (distal/type 1, type 4 hypoaldosteronism, proximal/type 2 variable). Reference range ≈ 0 to +40 mmol/L. Caveats: unreliable with unmeasured urine anions (ketoacidosis, toluene/hippurate, D-lactate) or when urine sodium < 25 mmol/L (use urine osmolar gap instead). Derived from Batlle CJASN 2012, Ito 2025, Bonner AJKD 2025. Interpret with blood gas and full clinical context. Not medical advice.

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Calculate the APACHE II (Acute Physiology and Chronic Health Evaluation II) ICU severity score. APACHE II = Acute Physiology Score (12 variables, each 0–4 using the worst value in the first 24 h) + Age points (0–6) + Chronic Health points (0/2/5). Range 0–71; higher scores indicate worse prognosis. Oxygenation uses the A-a gradient when FiO₂ ≥ 0.5, otherwise PaO₂. Creatinine points are doubled when acute renal failure is indicated. GCS contributes 15 − GCS. Also reports the base-model predicted mortality: R = 1/(1 + e^(−logit)), logit = −3.517 + 0.146 × score (diagnostic-category weight not included). Thresholds cross-verified against Knaus 1985 (Crit Care Med) and the SFAR scoring table. Not a substitute for clinical judgement. Not medical advice.

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Calculate the CHA₂DS₂-VASc score to stratify stroke risk in non-valvular atrial fibrillation and guide oral anticoagulation. Components: Congestive heart failure/LV dysfunction (+1), Hypertension (+1), Age ≥75 (+2), Diabetes (+1), prior Stroke/TIA/thromboembolism (+2), Vascular disease — prior MI/PAD/aortic plaque (+1), Age 65–74 (+1), Sex category female (+1). Range 0–9 (women) / 0–8 (men). Thresholds: men ≥2 or women ≥3 → recommend oral anticoagulation (DOAC preferred over warfarin); men 1 or women 2 → consider anticoagulation; men 0 or women ≤1 → omit. Female sex alone is not an independent risk factor (score 1 from sex alone is treated as 0). Includes an approximate annual stroke-risk estimate (Lip 2010 derivation cohort). Derived from Lip 2010 (Chest), 2019 AHA/ACC/HRS update, and 2023 ACC/AHA/ACCP/HRS AF guideline. Combine with bleeding risk (HAS-BLED) and shared decision-making. Not medical advice.