Ellipsoid Volume Calculator

Q: What prostate size is considered enlarged?

A prostate over about 30 cc is usually called enlarged. Doctors group it roughly like this: Under 30 cc: normal size 30–80 cc: moderate enlargement (BPH) Over 80 cc: large gland Size helps pick treatment. Drugs called 5-alpha reductase inhibitors work best on glands over 30–40 cc. Very large glands may need HoLEP or open surgery instead of a standard TURP.

Q: What is a normal testicular volume?

An adult testicle is usually 15 to 25 mL . Under about 12 mL is small and may point to low sperm or low testosterone. In boys, puberty starts when a testicle reaches about 4 mL. Doctors find the volume from an ultrasound using length × width × height × 0.52. Some use 0.71 instead, which fits the testis shape better and gives a larger number.

Q: How do you find tumor volume from length, width, and height?

Use the same ellipsoid math: V = 0.52 × L × W × H , with all three in centimeters. The answer is in cm³ (cc). Lab and animal studies often use a shortcut when only two measures are taken: V = 0.5 × L × W² . Tracking volume over time shows growth better than tracking one length, because volume changes with all three sides.

Q: What is a normal kidney volume?

One adult kidney is about 110 to 170 cc , with men on the higher end. Normal length is roughly 10 to 12 cm. Kidney volume is measured with length × width × depth × 0.52. It matters most in polycystic kidney disease, where total kidney volume is tracked over years, and before donating a kidney.

Ellipsoid Volume Calculator

Introduction

This Ellipsoid Volume Calculator finds the size of an egg-shaped object from three measurements: length, width, and height. Doctors use this math every day to measure the prostate, kidneys, bladder, thyroid, and cysts on ultrasound or CT scans.

The tool uses the standard ellipsoid formula, V = (π/6) × A × B × C. It also shows the bullet formula, V = (5π/24) × A × B × C, which many urologists prefer for prostate volume because the gland is not a perfect oval.

You can work both ways. Enter three axis lengths and leave the volume blank to get the volume. Or enter the volume and two axes, leave one axis blank, and the calculator solves for that missing axis. Pick your units: mm, cm, inches, feet, or meters for length, and cm³ (cc), mL, L, mm³, in³, ft³, or m³ for volume.

Each answer comes with the step-by-step math, so you can check the work. Two charts show how the ellipsoid and bullet results compare, and how the volume changes when one axis gets bigger or smaller.

How to use our Ellipsoid Volume Calculator

Enter three of the four fields below and leave one blank. The calculator finds the missing value and shows you the ellipsoid volume, the bullet volume, the math steps, and two charts.

Major Axis (Length) A: Type the full length of the shape from end to end, not half of it. Pick your unit (mm, cm, in, ft, or m) from the drop-down next to the box. Changing this unit changes it for all three axes.

Minor Axis (Width) B: Type the full width of the shape across its widest side. Use the same unit as the other axes.

Vertical Axis (Height) C: Type the full height of the shape from top to bottom. Again, use the full measure, not the semi-axis.

Volume V: Leave this box blank if you want the volume. If you already know the volume, type it in, pick a unit (mm³, cm³, mL, in³, ft³, m³, or L), and leave one axis blank instead. The calculator will solve for that axis.

Calculate and Reset: Click Calculate to see your results, or click Reset to clear the form and start over with the sample values.

What Is an Ellipsoid Volume?

An ellipsoid is a 3D shape like a squashed or stretched ball. An egg, a grape, and a football are all close to this shape. Many organs in the body are shaped this way too. To find the space inside an ellipsoid, you measure its three axes: length (A), width (B), and height (C). Then you use this formula:

Volume = (π ÷ 6) × A × B × C

This is often written as 0.52 × L × W × H, since π/6 is about 0.52. All three numbers must be full axis lengths, not half lengths (radii), and they must use the same unit. If you measure in centimeters, the answer comes out in cubic centimeters (cm³), which doctors call "cc." One cc equals one milliliter (mL).

Why Urologists Use This Formula

Doctors can't cut an organ open to measure it. Instead, they take three measurements on an ultrasound, CT, or MRI scan and use the ellipsoid formula. This is the standard way to find:

Prostate volume, measured by transrectal ultrasound (TRUS) or MRI
Bladder volume, to check how much urine is left after peeing (post-void residual)
Kidney and renal cyst size
Testicular volume, used to track growth and fertility
Tumor or mass size over time

Prostate Volume and PSA Density

A normal adult prostate is about 20 to 30 cc. As men get older, it often grows. This is called benign prostatic hyperplasia (BPH). A prostate over about 30 to 40 cc may press on the urethra and make it hard to pee. Size helps doctors pick the right drug or surgery.

Prostate volume is also used to find PSA density. That is the PSA blood level divided by the prostate volume. A big prostate makes more PSA on its own, so density helps tell normal growth apart from cancer risk. A PSA density above about 0.15 ng/mL/cc often leads to more testing.

The Bullet Formula

The ellipsoid formula can undercount the prostate, because a real prostate is not a perfect ellipsoid. The bullet formula fits the gland more closely:

Volume = (5π ÷ 24) × A × B × C, or about 0.654 × L × W × H

This gives a result about 25% larger than the ellipsoid formula. That is why this tool shows both numbers side by side.

Tips for Good Measurements

Measure all three axes at right angles to each other.
Use the same unit for all three axes.
Small errors matter a lot. Volume grows with all three sides, so a 10% error in one axis shifts the volume by about 10%.
Prostate weight in grams is close to volume in cc, since prostate tissue is about the same density as water.

This tool is for learning and quick math. It does not replace advice from a doctor.

Formulas used

Ellipsoid Volume

V_{ellipsoid} = \frac{\pi}{6} \cdot A \cdot B \cdot C

Bullet (Prolate) Volume

V_{bullet} = \frac{5\pi}{24} \cdot A \cdot B \cdot C

Solving for a Missing Axis

A = \frac{V}{\frac{\pi}{6} \cdot B \cdot C}

Unit Conversion (length to meters)

L_{SI} = L \times f_{length}

Unit Conversion (volume between units)

V_{target} = \frac{V_{source} \times f_{source}}{f_{target}}

Native Volume Unit Factor from Length Unit

f_{volume} = \left(f_{length}\right)^3

Frequently asked questions

Why does the ellipsoid volume formula use pi/6 instead of 4/3 pi?

Both formulas give the same answer. They just use different inputs.

V = 4/3 × π × a × b × c uses the three semi-axes (half lengths, like radii).
V = π/6 × A × B × C uses the three full axes (end to end).

Since each full axis is twice the semi-axis, 4/3 π divided by 2×2×2 gives π/6, or about 0.52. Doctors measure full lengths on a scan, so they use the π/6 version.

Is 1 cc the same as 1 mL?

Yes. One cubic centimeter (cm³ or cc) equals exactly one milliliter (mL). Doctors often say "cc" for organ size and "mL" for fluid, but the number does not change. So a 35 cc prostate is the same as a 35 mL prostate, and 1,000 cc equals 1 liter.

What is a normal prostate size by age?

The prostate grows slowly through adult life. Rough averages:

Ages 20–30: about 20 cc
Ages 40–50: about 25 cc
Ages 60–70: about 30–40 cc
Over 70: often 40 cc or more

Size alone does not mean trouble. Some men with a 60 cc prostate pee fine, and some with a 30 cc prostate have strong symptoms.

What prostate size is considered enlarged?

A prostate over about 30 cc is usually called enlarged. Doctors group it roughly like this:

Under 30 cc: normal size
30–80 cc: moderate enlargement (BPH)
Over 80 cc: large gland

Size helps pick treatment. Drugs called 5-alpha reductase inhibitors work best on glands over 30–40 cc. Very large glands may need HoLEP or open surgery instead of a standard TURP.

How is bladder volume measured on an ultrasound?

The tech measures the bladder in three directions: height, width, and depth. Then they multiply:

Bladder volume = 0.52 × H × W × D

That 0.52 is π/6, the ellipsoid factor. Some machines use a smaller factor, like 0.7 of the box volume, because a full bladder is rounder and an empty one is flatter. Measure in centimeters and the answer comes out in mL.

How much urine left in the bladder is too much?

Post-void residual (PVR) is the urine left right after you pee. General guides:

Under 50 mL: normal
50–100 mL: usually fine, watch it
100–200 mL: may point to a blockage or weak bladder
Over 300 mL: high, and can raise the risk of infection or kidney strain

One high reading is not proof of a problem. Doctors usually repeat the test.

What is a normal testicular volume?

An adult testicle is usually 15 to 25 mL. Under about 12 mL is small and may point to low sperm or low testosterone. In boys, puberty starts when a testicle reaches about 4 mL.

Doctors find the volume from an ultrasound using length × width × height × 0.52. Some use 0.71 instead, which fits the testis shape better and gives a larger number.

How do you find tumor volume from length, width, and height?

Use the same ellipsoid math: V = 0.52 × L × W × H, with all three in centimeters. The answer is in cm³ (cc).

Lab and animal studies often use a shortcut when only two measures are taken: V = 0.5 × L × W². Tracking volume over time shows growth better than tracking one length, because volume changes with all three sides.

What is a normal kidney volume?

One adult kidney is about 110 to 170 cc, with men on the higher end. Normal length is roughly 10 to 12 cm.

Kidney volume is measured with length × width × depth × 0.52. It matters most in polycystic kidney disease, where total kidney volume is tracked over years, and before donating a kidney.

What is a normal thyroid volume on ultrasound?

Each lobe is measured and calculated separately with length × width × depth × 0.52, then the two are added. The thin bridge between them (the isthmus) is usually skipped.

Normal totals are about 10–18 mL for women and 12–25 mL for men. Anything above that is called a goiter. Children have much smaller values that go up with age.

Why is prostate volume different on ultrasound and MRI?

The number can shift by 10–20% between scans. Common reasons:

The probe cuts the gland at a slightly different angle each time.
MRI shows the edges of the gland more clearly than ultrasound.
One report may use the ellipsoid factor (0.52) and another the bullet factor (0.654).

Because of this, doctors compare scans of the same type when they watch for growth.

How do you find the surface area of an ellipsoid?

There is no simple exact formula, so a close estimate is used. With semi-axes a, b, and c (half of each full axis):

S ≈ 4π × [ (a^pb^p + a^pc^p + b^pc^p) ÷ 3 ]^1/p, where p = 1.6075

This is within about 1% for most shapes. Volume, unlike surface area, does have an exact simple formula.

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