PSA Doubling Time Calculator

Q: How do you calculate PSA doubling time by hand?

With two readings, use this formula: PSADT = (time between tests) × 0.693 ÷ (ln PSA2 − ln PSA1) Here 0.693 is the natural log of 2, and "ln" is the natural log button on a scientific calculator. Example: PSA goes from 2.0 to 3.0 in 12 months. ln(3.0) − ln(2.0) = 0.405. So PSADT = 12 × 0.693 ÷ 0.405 = about 20.5 months. With three or more readings, doctors fit a line through the natural logs of all the values instead. That averages out lab noise.

Q: What is PSA nadir?

The nadir is the lowest PSA level you reach after treatment. It is the starting point doctors measure future rises from. A low nadir is generally a good sign. A nadir that stays high, or a PSA that starts climbing off the nadir, gets a closer look.

Q: What is a high PSA velocity?

A rise of more than 0.75 ng/mL per year has long been treated as a warning sign in men with PSA between 4 and 10 ng/mL. For men with lower PSA levels, a tighter cutoff of 0.35 ng/mL per year is sometimes used. Velocity is a straight-line speed. It works less well when PSA is very low, which is why doubling time is often used instead.

Q: How often should PSA be checked after prostate cancer treatment?

A common schedule is every 3 to 6 months for the first 5 years , then once a year after that. Men at higher risk may be tested more often. Tests spaced a few months apart over at least a year give the steadiest doubling time. Tests only weeks apart are often too close together to tell a real trend from normal lab wobble.

PSA Doubling Time Calculator

Introduction

The PSA Doubling Time Calculator shows how fast your PSA level is rising. PSA stands for prostate-specific antigen, a protein made by the prostate. Doctors track PSA with a simple blood test. When PSA goes up, the speed of that rise matters more than the number itself.

PSA doubling time (PSADT) is the time it takes for your PSA to double. A short doubling time means PSA is climbing fast. A long doubling time means it is climbing slowly. This tool also gives you PSA velocity, which is how many ng/mL your PSA gains each year.

To use it, add at least two PSA readings with their test dates. You can type them in one at a time, enter them by time gaps between tests, or paste a whole list at once. The calculator sorts your dates, fits a curve to your numbers using the log-linear regression method from the NCCN Guidelines, and shows the math step by step. You also get a chart and a check against two common clinical cutoffs: 9 months and 10 months.

More readings over a longer time give a better result. This tool is for learning and tracking only. Always talk with your doctor about what your numbers mean for you.

How to use our PSA Doubling Time Calculator

Enter at least two PSA test results with the dates they were taken, and the calculator will show your PSA doubling time in months and years, your PSA velocity, and a chart of your PSA trend.

Date: Pick the day the PSA blood test was drawn. Use the MM/DD/YYYY format.

PSA Value (ng/mL): Type the PSA number from that lab report. It must be higher than 0.1 ng/mL.

Add Entry: Click this to put the reading in the table. You can add dates in any order, and the table sorts them from oldest to newest.

Your PSA Readings table: Check your list here. Click "Remove" to delete one reading, or "Clear All" to erase them all.

PSA1 Value and Date of PSA1 (interval mode): If you do not know every test date, enter your first PSA value and the date it was taken.

Time since PSA1 and Unit: Enter how much time passed before the next test, then pick days, weeks, or months. Use "Add Another Measurement" for more readings, then click "Add These Readings to the Table."

Bulk Import: Paste many readings at once, one per line, like 01/15/2024, 1.20. Then click "Import Entries."

Calculate: Click this to get your PSA doubling time, PSA velocity, step-by-step math, and the fitted growth chart.

Reset: Click this to clear your work and load the sample data again.

What Is PSA Doubling Time?

PSA stands for prostate-specific antigen. It is a protein made by the prostate gland, and doctors measure it with a simple blood test. The result is given in nanograms per milliliter (ng/mL).

PSA doubling time (PSADT) is how long it takes for a man's PSA level to double. If your PSA goes from 2 ng/mL to 4 ng/mL in one year, your doubling time is about 12 months. A short doubling time means PSA is rising fast. A long doubling time means it is rising slowly.

Why PSA Doubling Time Matters

One PSA number by itself does not say much. The trend over time says a lot more. Prostate cancer cells often grow in an exponential way, so PSA rises in a curve, not a straight line. Tracking that curve helps doctors see how fast the disease is moving.

Doctors use PSADT to help with choices like:

Watching a slow cancer instead of treating it right away (active surveillance)
Deciding if cancer has come back after surgery or radiation
Judging the risk that cancer will spread to bone or other organs
Picking the right time to start or change treatment

How Doctors Read the Number

There is no single cutoff that fits everyone, but two numbers come up often in guidelines and drug trials:

PSADT of 9 months or less: NCCN guidelines call this high-risk biochemical recurrence after surgery or radiation. It points to a greater chance the cancer will spread.
PSADT of 10 months or less: Used in the SPARTAN, PROSPER, and ARAMIS trials to find men with non-metastatic castration-resistant prostate cancer (nmCRPC) who gain the most from newer hormone-blocking drugs.

Longer doubling times, such as more than 12 months, usually point to slower growth and lower risk. If PSA is going down instead of up, doubling time does not apply; the math gives a halving time instead.

PSA Velocity vs. PSA Doubling Time

PSA velocity is how many ng/mL the PSA climbs each year. It is a straight-line speed. Doubling time is a percent-based rate, so it works better when PSA levels are very small or very large. Doctors often look at both.

Getting Good Results

The math works best with clean data. A few things to watch:

Use at least three PSA tests; more tests give a steadier answer.
Spread tests over at least 6 to 12 months when you can.
Use the same lab if possible, since labs can differ.
Skip readings taken during an infection, after a prostate exam, or right after a biopsy, since these can push PSA up for a short time.
Very low PSA values (near or under 0.1 ng/mL) are noisy and can throw off the result.

Important Note

PSA doubling time is one piece of a bigger picture. Your Gleason score, stage, scans, age, and health all matter too. This number is a tool to help you talk with your doctor, not a diagnosis or a treatment plan on its own.

Formulas used

Log-linear regression of ln(PSA) vs time (NCCN method)

\ln \text{PSA}(t) = \ln a + \lambda t, \qquad \text{PSA}(t) = a\,e^{\lambda t}

Fitted exponential growth constant (OLS slope on log scale)

\lambda = \frac{m\sum t_i \ln y_i - \left(\sum t_i\right)\left(\sum \ln y_i\right)}{m\sum t_i^2 - \left(\sum t_i\right)^2}, \qquad \ln a = \frac{\sum \ln y_i - \lambda \sum t_i}{m}

PSA doubling time (days)

t_d = \frac{\ln 2}{\lambda} = \frac{0.693147}{\lambda}

Doubling time in months and years

t_{d,\text{mo}} = \frac{t_d}{30.4375}, \qquad t_{d,\text{yr}} = \frac{t_d}{365.25}

PSA velocity (OLS slope of PSA vs time in years)

V_{\text{yr}} = \frac{n\sum t_i y_i - \left(\sum t_i\right)\left(\sum y_i\right)}{n\sum t_i^2 - \left(\sum t_i\right)^2}, \qquad V_{\text{mo}} = \frac{V_{\text{yr}}}{12}

Goodness of fit on log scale

R^2 = 1 - \frac{\sum \left(\ln y_i - \left(\ln a + \lambda t_i\right)\right)^2}{\sum \left(\ln y_i - \overline{\ln y}\right)^2}

Total time span between first and last reading

\Delta t = \frac{t_{\text{last}} - t_{\text{first}}}{86400000}\ \text{days}, \qquad \Delta t_{\text{mo}} = \frac{\Delta t}{30.4375}

Frequently asked questions

How do you calculate PSA doubling time by hand?

With two readings, use this formula:

PSADT = (time between tests) × 0.693 ÷ (ln PSA2 − ln PSA1)

Here 0.693 is the natural log of 2, and "ln" is the natural log button on a scientific calculator.

Example: PSA goes from 2.0 to 3.0 in 12 months. ln(3.0) − ln(2.0) = 0.405. So PSADT = 12 × 0.693 ÷ 0.405 = about 20.5 months.

With three or more readings, doctors fit a line through the natural logs of all the values instead. That averages out lab noise.

What PSA level means prostate cancer has come back after surgery?

After a radical prostatectomy, PSA should drop to almost zero because the prostate is gone. Most guidelines call it biochemical recurrence when PSA reaches 0.2 ng/mL or higher on two tests in a row.

That does not always mean the cancer has spread. It means some prostate cells are still making PSA. How fast the number rises after that is what helps doctors judge the risk.

What counts as prostate cancer recurrence after radiation?

Radiation leaves the prostate in place, so PSA never falls to zero. Doctors use the Phoenix definition: recurrence is when PSA rises 2 ng/mL above the lowest level (the nadir) reached after treatment.

Example: if your lowest PSA was 0.5 ng/mL, recurrence is flagged at 2.5 ng/mL.

What is PSA nadir?

The nadir is the lowest PSA level you reach after treatment. It is the starting point doctors measure future rises from.

A low nadir is generally a good sign. A nadir that stays high, or a PSA that starts climbing off the nadir, gets a closer look.

What is a high PSA velocity?

A rise of more than 0.75 ng/mL per year has long been treated as a warning sign in men with PSA between 4 and 10 ng/mL. For men with lower PSA levels, a tighter cutoff of 0.35 ng/mL per year is sometimes used.

Velocity is a straight-line speed. It works less well when PSA is very low, which is why doubling time is often used instead.

What else can make PSA go up besides cancer?

Plenty of things raise PSA for a short time:

An enlarged prostate (BPH), which is common with age
Prostate infection or inflammation (prostatitis)
A urinary tract infection
A recent prostate biopsy or catheter
A digital rectal exam
Riding a bike or ejaculating in the last day or two

A single odd reading from one of these can make a doubling time look much worse than it is.

What is a normal PSA level by age?

PSA tends to climb slowly with age. Common reference ranges are:

40–49: up to 2.5 ng/mL
50–59: up to 3.5 ng/mL
60–69: up to 4.5 ng/mL
70–79: up to 6.5 ng/mL

These are guides, not hard rules. Men with prostate cancer already treated are judged against their own past numbers, not these ranges.

How often should PSA be checked after prostate cancer treatment?

A common schedule is every 3 to 6 months for the first 5 years, then once a year after that. Men at higher risk may be tested more often.

Tests spaced a few months apart over at least a year give the steadiest doubling time. Tests only weeks apart are often too close together to tell a real trend from normal lab wobble.

Does a short PSA doubling time mean cancer has spread?

No. A short doubling time means PSA is rising fast, which raises the chance that cancer has spread. It is not proof.

Doctors confirm spread with imaging, such as a bone scan, CT, MRI, or a PSMA PET scan. A fast doubling time is often the reason those scans get ordered.

Can PSA doubling time change over time?

Yes. Doubling time is a snapshot of the readings you feed into it. Adding new tests can shorten or lengthen the answer.

Cancer growth can also speed up or slow down, and treatment can reset the whole trend. Because of this, doctors usually recalculate doubling time as each new result comes in.

What is nmCRPC and why does doubling time matter for it?

nmCRPC stands for non-metastatic castration-resistant prostate cancer. It means PSA keeps rising even though hormone therapy has pushed testosterone very low, and scans show no spread.

The SPARTAN, PROSPER, and ARAMIS trials enrolled men with a PSA doubling time of 10 months or less, because those men faced the highest risk of the cancer spreading. That cutoff still guides treatment choices today.

What is a PSA bounce after radiation?

A bounce is a short, harmless rise in PSA that happens in some men 12 to 24 months after radiation or seed implants. PSA goes up by a small amount, then falls back down on its own.

A bounce can make a doubling time look alarming when nothing is wrong. Doctors usually repeat the test in a few months before acting on a single rise.

Why is PSA doubling time based on exponential math instead of a straight line?

Cancer cells divide, so the number of cells tends to multiply rather than add. That makes PSA rise in a curve that gets steeper over time.

Taking the natural log of each PSA value turns that curve into a straight line. The slope of that line, divided into 0.693 (the natural log of 2), gives the doubling time. This log-linear method is the one named in the NCCN guidelines.

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