Renal Clearance Equations: GFR, PAH & Filtration Fraction

Renal clearance is C = UV/P (urine concentration × urine flow rate ÷ plasma concentration): the volume of plasma completely cleared of a substance per minute (mL/min). Inulin clearance equals GFR (about 120 mL/min), PAH clearance equals effective renal plasma flow (about 600 mL/min), and filtered load equals GFR × plasma concentration.

Compare a clearance with the GFR to see what the tubule did: equal means filtered only, lower means net reabsorption, higher means net secretion. Check units first: U and P must match, and V must be in mL/min.

Drug (pharmacokinetic) clearance is covered in the drug clearance question breakdown.

Renal clearance formulas at a glance

The renal clearance equation: C = UV/P

$C_x = \frac{U_x \times V}{P_x}$

• $U_x$ is the urine concentration, $V$ the urine flow rate (24-hour volume ÷ 1,440 minutes) and $P_x$ the plasma concentration. U and P cancel, so they must share units, leaving mL/min.
• $U_x \times V$ is the excretion rate; the equation assumes a steady state, with stable plasma levels during the collection.
• Example: urine creatinine 120 mg/dL, V = 1 mL/min, plasma creatinine 1.0 mg/dL: $C_{Cr}$ = 120 mL/min. Enter urine creatinine as 1.2 mg/mL against 1.0 mg/dL in plasma and you get 1.2 mL/min, a 100-fold error.

Filtered load formula: excretion, reabsorption and secretion

$\text{Filtered load} = GFR \times P_x$

• Only unbound solute is filtered. About 40% of serum calcium is protein-bound, so calcium's filtered load is GFR × its ultrafilterable fraction (about 60%); even phosphate is only about 90% ultrafilterable.
• Excretion = $U_x \times V$; net reabsorption = filtered load − excretion; net secretion = excretion − filtered load.

Glucose threshold and transport maximum ($T_m$). Reabsorption rises with filtered load until the transporters saturate: about 375 mg/min in men and 300 in women (OpenStax), though StatPearls gives 0.9–2.0 mmol/min (about 160–360 mg/min). Glucosuria starts above about 180 mg/dL, the commonly accepted renal threshold (Merck: 160–180; OpenStax: about 200). At 400 mg/dL, the filtered load is 500 mg/min; with a $T_m$ of 375, about 125 mg/min is excreted, a glucose clearance of about 31 mL/min, still below GFR.

• Pregnancy lowers the threshold; age and diabetic glomerulosclerosis raise it.
• SGLT2 handles over 90% of glucose reabsorption, so SGLT2 inhibitors lower the threshold and raise glucose clearance (tubular reabsorption and secretion breakdown).

PAH clearance formula: effective RPF, true RPF and RBF

$C_{PAH} = \frac{U_{PAH} \times V}{P_{PAH}} \approx \text{effective RPF}$

• PAH (para-aminohippurate) is filtered and actively secreted by the proximal tubule via the organic anion transporters OAT1 and OAT3. At low plasma levels (1–2 mg/dL), an average of 90% is removed from renal blood in one pass, so PAH clearance is effective RPF, slightly below true RPF.
• Extraction ratio: $E_{PAH} = (P_a - P_{rv}) / P_a$ (arterial and renal venous PAH); true RPF = $C_{PAH} / E_{PAH}$, which needs a renal vein sample.
• Renal blood flow: RBF = RPF / (1 − Hct).

Worked example: arterial PAH 0.02 mg/mL, renal vein PAH 0.002 mg/mL, urine PAH 9 mg/mL, V = 1.2 mL/min, hematocrit 40%.

1. $C_{PAH}$ = 9 × 1.2 / 0.02 = 540 mL/min (effective RPF)
2. $E_{PAH}$ = (0.02 − 0.002) / 0.02 = 0.90
3. True RPF = 540 / 0.90 = 600 mL/min
4. RBF = 600 / (1 − 0.40) = 1,000 mL/min
5. With a GFR of 120 mL/min, FF = 120 / 600 = 0.20 (0.22 with effective RPF)

PAH clearance underestimates RPF when plasma PAH is high (40–60 mg/dL saturates secretion; used to measure $T_m$PAH), when competing organic anions are present (probenecid, penicillin, salicylates), and when tubules are injured: extraction is not constant in sepsis or AKI, and after renal ischemia in rats, uncorrected PAH clearance underestimated RPF about threefold.

Inulin clearance formula and measured GFR

$GFR = C_{inulin} = \frac{U_{inulin} \times V}{P_{inulin}}$

• Why inulin: a plant polysaccharide that is freely filtered and not reabsorbed, secreted, made or metabolized by the kidney; because it needs a continuous infusion, it is used mostly in research.
• Example: plasma 0.25 mg/mL, urine 25 mg/mL, V = 1.25 mL/min: GFR = 25 × 1.25 / 0.25 = 125 mL/min.
• Normal values: 120–130 mL/min/1.73 m² in young adults, about 75 by age 70; roughly 180 L of filtrate a day in men, about 99% of it reabsorbed. Indexing to 1.73 m² of body surface area compares people of different size. In pregnancy, GFR rises 30–50% and creatinine falls to about 0.5–0.7 mg/dL.
• Today's gold standard (KDIGO 2024) is measured GFR (mGFR): urinary or plasma clearance of iohexol, iothalamate, chromium-51 EDTA or technetium-99m DTPA. Plasma methods need no urine collection.

Creatinine clearance and eGFR: CKD-EPI 2021 vs the classic answer

Why creatinine clearance overestimates GFR: creatinine, made from muscle creatine at a fairly steady rate, is freely filtered and also secreted by the tubules, so $C_{Cr}$ exceeds GFR by about 10–20% with normal kidney function and by up to 50% in advanced kidney failure.

24-hour collection, worked: 1,440 mL in 24 hours (V = 1 mL/min), urine creatinine 120 mg/dL, serum creatinine 1.0 mg/dL: $C_{Cr}$ = 120 mL/min. That is 1,728 mg/day of creatinine, about 25 mg/kg/day for a 70-kg man (normal 14–26 in men, 11–20 in women); lose half the urine and the result falls to a falsely low 60 mL/min. KDIGO 2024 calls timed collections "highly prone to errors" (mean bias 25%, in both directions) and reserves them for when mGFR is unavailable and the creatinine-cystatin C estimate seems inaccurate.

Serum creatinine traps:

• At steady state, production equals excretion (about GFR × plasma creatinine): doubling serum creatinine means GFR has roughly halved, and creatinine can stay normal until about half of kidney function is lost.
• Muscular people run higher levels, older or undernourished people lower ones; a cooked-meat meal can add about 0.23 mg/dL.
• Blocked secretion raises creatinine without changing GFR: trimethoprim (by about 15–22%), cimetidine, dolutegravir. On dolutegravir, 24-hour creatinine clearance fell 9–13% while iohexol GFR and PAH clearance were unchanged; its label cites inhibition of OCT2 (and possibly MATE1).

CKD-EPI 2021 uses serum creatinine (mg/dL), age and sex, with no race term, and reports mL/min/1.73 m²:

$eGFR = 142 \times \min\left(\frac{S_{cr}}{\kappa}, 1\right)^{\alpha} \times \max\left(\frac{S_{cr}}{\kappa}, 1\right)^{-1.200} \times 0.9938^{\text{Age}} \times 1.012\ (\text{if female})$

κ is 0.7 for women and 0.9 for men; α is −0.241 for women and −0.302 for men. For a 60-year-old man with creatinine 1.2 mg/dL: 142 × 0.708 × 0.689 ≈ 69 mL/min/1.73 m²; the same creatinine in a 60-year-old woman gives about 52.

Cockcroft-Gault, the classic formula, estimates creatinine clearance in mL/min, not indexed to body size:

$C_{Cr} = \frac{(140 - \text{age}) \times \text{weight (kg)}}{72 \times S_{cr}} \times 0.85\ (\text{if female})$

A 72-year-old, 60-kg man with creatinine 1.3 mg/dL: 68 × 60 / (72 × 1.3) ≈ 44 mL/min, against a CKD-EPI 2021 eGFR of about 58. KDIGO notes that it predates standardized creatinine assays and relies on weight, which edema and obesity distort.

• Cystatin C, made by all nucleated cells, is filtered, then reabsorbed and broken down by the proximal tubule, so it is a serum marker, not a urine clearance. Muscle barely affects it; adiposity, smoking, thyroid disease, glucocorticoid excess and inflammation do.
• CKD stages (G1 to G5) are set by eGFR (CKD stages mnemonic); marker-choice questions are in the GFR estimation question breakdown.

Filtration fraction: the ratio of GFR to RPF

$FF = \frac{GFR}{RPF} \approx \frac{120}{600} = 0.20$

About 20% of the plasma reaching the glomeruli is filtered; a higher FF leaves more concentrated protein in the peritubular capillaries and increases proximal reabsorption. Use plasma flow, not blood flow. Net filtration pressure is glomerular capillary pressure − (Bowman's space pressure + capillary oncotic pressure), about 55 − (15 + 30) = 10 mm Hg.

• ACE inhibitors and ARBs cut GFR most when angiotensin II is propping it up: renal artery stenosis (bilateral or in a solitary kidney), volume depletion or diuretics; adding an NSAID is a relative contraindication (ACE inhibitor and ARB mnemonic).
• SGLT2 inhibitors raise distal sodium delivery, increasing tubuloglomerular feedback and lowering intraglomerular pressure: expect a small, reversible early eGFR dip.
• ANP dilates the afferent and constricts the efferent arteriole, raising GFR (renal blood flow autoregulation).

Fractional excretion: FENa and FEUrea

$FE_x\ (\%) = \frac{U_x \times P_{Cr}}{P_x \times U_{Cr}} \times 100$

FE is the clearance of x divided by the creatinine clearance; urine flow cancels, so a spot urine sample works.

• FENa below 1% suggests prerenal AKI (tubules holding on to sodium); above 2% suggests acute tubular necrosis (Merck uses above 1%). Other prerenal clues: urine sodium below 20 mEq/L and BUN:creatinine above 20 (below 10 in tubular injury).
• FEUrea below 35% suggests prerenal and above 50% intrinsic AKI; use it in patients taking diuretics.
• Worked: urine Na 20 mEq/L, plasma Na 140, urine creatinine 100 mg/dL, plasma creatinine 2.0: FENa = (20 × 2.0)/(140 × 100) × 100 = 0.29%. Urine Na 60, plasma Na 135, urine creatinine 40, plasma creatinine 4.0: 4.4%.

No single marker reliably separates the causes of AKI (StatPearls, 2026); see prerenal vs intrinsic vs postrenal AKI.

Free water clearance

$C_{osm} = \frac{U_{osm} \times V}{P_{osm}} \qquad C_{H_2O} = V - C_{osm}$

$C_{H_2O}$ is solute-free water excreted per minute; a negative value is free water reabsorption ($T^c_{H_2O} = C_{osm} - V$).

Worked: V = 10 mL/min, urine 100 and plasma 290 mOsm/kg: $C_{osm}$ = 3.4 mL/min, so $C_{H_2O}$ = +6.6 mL/min. SIADH with V = 0.5 mL/min, urine 600 and plasma 270 mOsm/kg: −0.6 mL/min. AVP deficiency and AVP resistance are the new names for central and nephrogenic DI (central vs nephrogenic diabetes insipidus).

Electrolyte-free water clearance uses urinary sodium and potassium instead of total osmolality:

$C^{e}_{H_2O} = V \times \left(1 - \frac{U_{Na} + U_K}{P_{Na}}\right)$

• A Furst ratio, $(U_{Na} + U_K)/P_{Na}$, above 1 suggests fluid restriction alone will fail, though in a 2025 prospective study it predicted failure only modestly (AUC 0.65). Plasma Na 125 with urine Na + K 160 mEq/L gives 1.28: at 1 mL/min, $C^{e}_{H_2O}$ = −0.28 mL/min.
• A positive value is not automatically reassuring: a 2026 review says values above about 500–800 mL/day predict a response to fluid restriction (SIADH vs psychogenic polydipsia).
• Thiazides act in the distal convoluted tubule and impair free water generation; they are the most common cause of drug-induced hyponatremia needing admission (thiazide mnemonic).

USMLE traps: classic teaching vs current evidence

More renal topics are on the Nephrology hub.

Worked USMLE-style vignettes

Vignette 1: inulin, PAH and substance X. A volunteer receives continuous inulin and PAH infusions; urine flow is 2 mL/min. Inulin: plasma 0.5 mg/mL, urine 30 mg/mL. PAH: plasma 0.02 mg/mL, urine 6 mg/mL. Substance X (freely filtered): plasma 1 mg/mL, urine 30 mg/mL. Which statement is correct?

• A. GFR 120 mL/min, FF 0.20, net reabsorption of X 60 mg/min
• B. GFR 120 mL/min, FF 0.20, net secretion of X 60 mg/min
• C. GFR 60 mL/min, FF 0.10, X filtered only
• D. GFR 600 mL/min, FF 5.0, net reabsorption of X
• E. GFR 120 mL/min, FF 0.50, X completely reabsorbed

Answer: A. $C_{inulin}$ = 30 × 2 / 0.5 = 120 mL/min; $C_{PAH}$ = 6 × 2 / 0.02 = 600 mL/min, so FF = 0.20. X: filtered 120 mg/min, excreted 60 mg/min, so 60 mg/min is reabsorbed.

• B: excretion is below the filtered load, so X was reabsorbed.
• C: 60 mL/min is the clearance of X, not the GFR.
• D: 600 mL/min is the PAH clearance; FF cannot exceed 1.
• E: complete reabsorption would leave no X in the urine.

Vignette 2: creatinine rise on a new drug. A 34-year-old man with HIV starts a dolutegravir-based regimen. Four weeks later his creatinine has risen from 0.90 to 1.05 mg/dL and stays there; blood pressure, potassium and urinalysis are normal, and iohexol GFR is unchanged. What explains the rise?

• A. Afferent arteriolar constriction
• B. Efferent arteriolar dilation
• C. Acute interstitial nephritis
• D. Inhibition of tubular creatinine secretion
• E. Increased creatinine generation by muscle

Answer: D. Dolutegravir blocks creatinine secretion (OCT2, possibly MATE1); its label reports an early, stable creatinine rise with unchanged iohexol GFR and PAH clearance.

• A and B: both lower GFR (the NSAID and ACE inhibitor patterns), but measured GFR did not change.
• C: kidney injury would lower GFR.
• E: nothing suggests more muscle or creatine intake.

Vignette 3: FENa on furosemide. A 76-year-old woman with heart failure takes furosemide and has eaten poorly for a week. Creatinine is 2.0 mg/dL (baseline 1.0), BUN 56 mg/dL, plasma sodium 134 mEq/L. Spot urine: sodium 64 mEq/L, creatinine 40 mg/dL, urea nitrogen 280 mg/dL, a few hyaline casts. Ultrasound shows no hydronephrosis or retained urine. Most likely cause of her AKI?

• A. Acute tubular necrosis
• B. Prerenal AKI
• C. Postrenal obstruction
• D. Acute interstitial nephritis
• E. Rapidly progressive glomerulonephritis

Answer: B. FENa = (64 × 2.0)/(134 × 40) × 100 = 2.4%, but furosemide raises urinary sodium. FEUrea = (280 × 2.0)/(56 × 40) × 100 = 25% (below 35%), and BUN:creatinine is 28: prerenal.

• A: the high FENa is a diuretic effect; FEUrea argues against tubular necrosis.
• C: no hydronephrosis or retained urine.
• D: furosemide can cause interstitial nephritis, but there is no rash or abnormal sediment.
• E: no red cell casts or dysmorphic red cells.

Key takeaways

• C = UV/P in mL/min, with U and P in the same units; versus GFR: equal = filtered only, lower = net reabsorption, higher = net secretion.
• Filtered load = GFR × unbound plasma concentration; reabsorption = filtered − excreted; secretion = excreted − filtered.
• Inulin (or iohexol) clearance = GFR; creatinine clearance overestimates it by 10–20% (secretion). Clinically: race-free eGFR, then cystatin C, then measured GFR.
• PAH clearance = effective RPF (about 600 mL/min); true RPF = $C_{PAH}$ / extraction; RBF = RPF / (1 − Hct); FF = GFR / RPF (about 0.20).
• FENa below 1% suggests prerenal AKI, above 2% tubular necrosis; on diuretics, use FEUrea (below 35% = prerenal).
• $C_{H_2O} = V - C_{osm}$: positive with dilute urine, negative with concentrated urine.

Sources

• Physiology, Glomerular Filtration Rate — StatPearls (2023)
• Physiology, Renal Blood Flow and Filtration — StatPearls (2023)
• Creatinine Clearance — StatPearls (2024)
• Renal Function Tests — StatPearls (2024)
• Physiology, Glycosuria — StatPearls (2023)
• Prerenal Kidney Failure — StatPearls (2023)
• Acute Kidney Injury — StatPearls (2026)
• Physiology, Calcium — StatPearls (2026)
• Angiotensin-Converting Enzyme Inhibitors — StatPearls (2023)
• Syndrome of Inappropriate Antidiuretic Hormone Secretion — StatPearls (2023)
• Glucosuria — Clinical Methods (1990)
• BUN and Creatinine — Clinical Methods (1990)
• Urinary Clearance Measurements — National Research Council (1995)
• Primary Disorders of Phosphate Metabolism — Endotext (2025)
• The Neurohypophysis — Endotext (2025)
• Free Water Clearance Definitions — Laboratory Manual of Kidney Perfusion Techniques (2017)
• KDIGO 2024 CKD Guideline — Kidney International (2024)
• CKD-EPI Creatinine Equation (2021) — National Kidney Foundation
• Inker LA, et al. GFR Equations without Race — N Engl J Med (2021)
• Delgado C, et al. NKF-ASN Task Force on GFR Estimation — Am J Kidney Dis (2022)
• Evaluation of the Patient With Renal Issues — Merck Manual (2025)
• Acute Kidney Injury — Merck Manual (2026)
• Physiology of Pregnancy — Merck Manual (2024)
• Type 1 Diabetes Mellitus — Merck Manual (2025)
• 25.5 Physiology of Urine Formation — OpenStax (2022)
• 25.6 Tubular Reabsorption — OpenStax (2022)
• 25.8 Endocrine Regulation of Kidney Function — OpenStax (2022)
• p-Aminohippuric Acid — PubChem, NLM
• Bischoff A, et al. PAH Clearance After Renal Ischemia — Physiol Rep (2014)
• Langenberg C, et al. Renal Blood Flow in Sepsis — Crit Care (2005)
• Guasch A, Myers BD. Hypofiltration in Minimal Change Nephropathy — J Am Soc Nephrol (1994)
• Martínez-Sánchez FD, et al. Hyponatremia: Evolving Diagnostics — World J Nephrol (2026)
• Chienwichai K, et al. Urine Electrolytes and Fluid Restriction in SIAD — Kidney360 (2025)
• Nadal J, et al. Thiazide-Induced Hyponatremia — Curr Hypertens Rep (2018)
• Tivicay (dolutegravir) label — DailyMed (2026)
• Jardiance (empagliflozin) label — DailyMed (2026)