MAGENT

PSA density (PSAD): formula and examples (Benson 1992)

PSA density (PSAD) is the serum prostate-specific antigen (PSA) divided by the volume of the prostate. A large benign gland can make more PSA than a small one, so dividing by volume helps separate PSA that may simply reflect gland size from PSA that is high for the size. Magent's PSA density calculator takes PSA in ng/mL and either a prostate volume in mL or three dimensions in cm, and returns PSAD to three decimal places with Benson's group.

Not a medical device. Not a diagnosis or dosing recommendation.

Use this calculator via API

What is PSA density?

PSA rises with prostate cancer, but also with benign enlargement of the prostate. Benson and colleagues proposed PSA density in 1992 as a way to tell the two apart better in men whose PSA was raised. They looked back at a series of patients and compared PSAD between benign enlargement and cancer.

Volume can come from imaging such as transrectal ultrasound. If you give three dimensions, the calculator uses Benson's simple formula, length × width × depth × 0.5.

The PSA density formula

prostate volume (mL) = length (cm) x width (cm) x depth (cm) x 0.5
                       or a measured volume you supply

PSAD = PSA (ng/mL) / prostate volume (mL)      3 decimal places

Benson group (from the rounded PSAD):
  <=0.05       0.05 or less
  0.05-0.10    above 0.05 and below 0.10
  >=0.10       0.10 or more

Exact expression the calculator uses:

volume_ml = length_cm × width_cm × depth_cm × 0.5 (Benson: D1×D2×D3×1/2, not π/6); psad = psa_ng_ml / volume_ml

Inputs

InputMeaningRange
psa_ng_mlSerum PSA in ng/mL0.01 to 10000
prostate_volume_mlProstate volume in mL, if measured1 to 500
length_cm, width_cm, depth_cmThree prostate dimensions in cm, if no volume1 to 20 each

Give either the volume or all three dimensions, not both. Out-of-range values return invalid_psa or invalid_prostate_dimension, and a missing volume, or both a volume and dimensions, returns invalid_psad.

How the calculation works

  1. Volume. Use the measured volume, or multiply length × width × depth × 0.5.
  2. Divide. PSA ÷ volume.
  3. Round. PSAD is given to three decimal places.
  4. Group. The rounded PSAD is placed in one of Benson's three groups.

PSAD has units of ng/mL per mL of prostate.

Units

PSA in ng/mL is the same number as µg/L. Volume in mL is the same as cm³.

Worked examples

These use Magent's own expected values for the calculator.

Example 1: PSA 4 with a 50 mL gland

  1. 4 ÷ 50.
  2. PSAD 0.08, group 0.05-0.10.

Example 2: PSA 2 with a 25 mL gland

  1. 2 ÷ 25.
  2. PSAD 0.08, group 0.05-0.10. Half the PSA in half the volume gives the same density.

Example 3: volume from three 4 cm dimensions

  1. Volume 4 × 4 × 4 × 0.5 = 32.0 mL.
  2. PSA 4 ÷ 32.0 = 0.125, group >=0.10.

Example 4: PSA 2 with a 40 mL gland

  1. 2 ÷ 40.
  2. PSAD 0.05, group <=0.05, since 0.05 sits in the lower group.

Example 5: PSA 0.5 with a 50 mL gland

  1. 0.5 ÷ 50.
  2. PSAD 0.01, group <=0.05.

Example 6: PSA 20 with a 10 mL gland

  1. 20 ÷ 10.
  2. PSAD 2.0, group >=0.10.

History of PSA density

Benson MC, Whang IS, Pantuck A, Ring K, Kaplan SA, Olsson CA and Cooner WH published the idea in the Journal of Urology in 1992, in "Prostate specific antigen density: a means of distinguishing benign prostatic hypertrophy and prostate cancer". The study was retrospective. Its three groups describe what was seen in that series, not a rule for further tests. Thresholds used in practice today come from later studies, not from this paper.

When it's used

PSAD is worked out when a man has a PSA result and a prostate volume, usually from imaging, to put the PSA in the context of gland size.

Where it's used

Urology clinics, imaging departments and primary care.

Who uses it

Urologists, radiologists and general practitioners. The calculator works out the volume if needed and does the division.

Limits of the calculation

  • Volume estimates vary with the imaging method and the person measuring.
  • The 0.5 formula is a simple approximation of a gland's shape.
  • Benson's groups come from a retrospective series.
  • The calculator doesn't decide on a biopsy or any other test.
  • This page doesn't say what a result means for a particular person.

Clinical decisions belong to a qualified clinician who knows the patient.

  • Gleason grades prostate cancer tissue under the microscope.
  • D'Amico groups prostate cancer risk from PSA, Gleason and stage.
  • CAPRA scores prostate cancer risk using PSA, Gleason, stage, the share of positive biopsy cores and age.

Glossary

  • PSA: prostate-specific antigen, a protein made by the prostate.
  • Benign prostatic hypertrophy: non-cancerous enlargement of the prostate.
  • Transrectal ultrasound: an ultrasound scan of the prostate through the rectum.
  • Retrospective: a study that looks back at existing records.

Common mistakes

  • Using π/6 in the volume. This calculator follows Benson's 0.5.
  • Giving both a volume and dimensions. Use one or the other.
  • Mixing units. PSA in ng/mL, dimensions in cm, volume in mL.
  • Treating a group as a test decision. The groups describe one historical series.

Source

Benson MC, et al. Prostate specific antigen density: a means of distinguishing benign prostatic hypertrophy and prostate cancer. J Urol. 1992;147(3 Pt 2):815-816. DOI: 10.1016/s0022-5347(17)37393-7. PMID: 1371554

Frequently asked questions

How do you calculate PSA density?

Divide PSA in ng/mL by prostate volume in mL.

Why does the volume use 0.5 instead of pi/6?

Benson's paper used length × width × depth × 0.5. Other sources use π/6, which is slightly larger and gives a slightly larger volume. This calculator follows Benson.

What PSA density is high?

Benson's series grouped results as 0.05 or less, between 0.05 and 0.10, and 0.10 or more. The calculator reports that group. Later studies use other thresholds, which aren't applied here.

Can I enter the prostate volume directly?

Yes, from 1 to 500 mL.

What units does PSAD use?

ng/mL of PSA per mL of prostate.