Total Magnification Formula: How to Calculate It

This calculator works out the total magnification of a microscope or other optical system. You enter the magnification of the eyepiece (ocular lens) and the objective lens, and it returns the combined magnification. You’ll need the magnification values printed on the lenses, which are usually marked like 10x, 40x, or 100x.

Formula

The total magnification is the product of the eyepiece magnification and the objective magnification:

Total Magnification = Eyepiece Magnification × Objective Magnification

In symbols:

M_total = M_eyepiece × M_objective

Where:

• M_total is the total magnification (unitless, often written as ×, e.g., 400×)
• M_eyepiece is the magnification of the eyepiece (e.g., 10×)
• M_objective is the magnification of the objective lens (e.g., 40×)

This formula applies to compound light microscopes, stereo microscopes, and other systems where the magnifications of two lenses multiply.

Worked Example

Using the default values from the calculator:

Eyepiece magnification = 10×, Objective magnification = 40×.

Step 1: Write down the formula: M_total = M_eyepiece × M_objective

Step 2: Substitute the values: M_total = 10 × 40

Step 3: Multiply: M_total = 400

So the total magnification is 400×.

When to Use This

Use this formula whenever you need to know the total magnification of a microscope for a given combination of eyepiece and objective lenses. This is essential for:

• Recording observations in a lab notebook (always note the total magnification).
• Comparing images taken at different magnifications.
• Estimating the size of a specimen when you know the field of view at a certain magnification.
• Choosing the right lens combination for a specific viewing task.

How to Read the Result

The result is a number followed by “×” (times). For example, 400× means the image appears 400 times larger than the actual size of the specimen. A higher total magnification lets you see smaller details, but it also reduces the field of view and may require more light.

Common Mistakes

• Forgetting to multiply: Some people add the magnifications instead of multiplying. Always multiply.
• Using the wrong values: Check that you are using the magnification of the eyepiece and the objective, not the numerical aperture (NA) or other numbers printed on the lens.
• Ignoring the “×” symbol: The magnification is unitless, but it is conventionally written with a multiplication sign (e.g., 10×). Do not confuse this with the multiplication operator in the formula.
• Mixing up eyepiece and objective: The eyepiece is the lens you look through; the objective is the lens closest to the specimen. Both are needed.

Tips

• Always check the magnification markings on your specific lenses – they can vary even within the same brand.
• When writing results, use the format “400×” (not just “400”).
• If your microscope has a zoom or variable magnification, use the current setting.
• For digital microscopes or cameras, the total magnification may also include a camera adapter factor – check your manual.

Troubleshooting

If your calculated total magnification seems too high or too low, check the following:

• Re-read the lens markings: Some objectives have markings like “40/0.65” where 0.65 is the numerical aperture, not the magnification. Use the number before the slash.
• Check for an additional magnification factor: Some microscopes have a built-in magnification changer (e.g., 1.5×) that you must include. Multiply all factors together.
• Verify you are not using the oil immersion objective incorrectly: If you are using a 100× oil objective without oil, the image will be poor, but the magnification is still 100×.
• If the result is a decimal: Make sure you entered whole numbers correctly. Magnifications are usually whole numbers.

Frequently Asked Questions

What does “10×” mean on a lens?

It means the lens magnifies the image 10 times. So an object appears 10 times larger than its actual size when viewed through that lens alone.

Do I need to include the microscope’s tube length?

No, the tube length is already accounted for in the magnification values printed on the lenses. You only multiply the eyepiece and objective magnifications.

What is the total magnification if I use a 10× eyepiece and a 100× objective?

It is 10 × 100 = 1000×. This is a common high-power combination.

Why is my total magnification different from what I expected?

Check if your microscope has an additional magnification factor (like a zoom or a binocular head factor). Multiply all factors together. Also, verify the objective magnification – some objectives are 20×, not 40×.

Can I use this formula for a stereo microscope?

Yes, but stereo microscopes often have a zoom knob that changes the objective magnification continuously. Use the current zoom setting as the objective magnification.

Does total magnification affect resolution?

Total magnification is separate from resolution. Resolution is the ability to distinguish two close points, and it is determined by the numerical aperture and wavelength of light. Increasing magnification beyond a certain point (empty magnification) does not improve resolution.

Related

• How to Calculate Molarity in Chemistry
• How to Calculate Ocular Magnification
• Objective Lens Magnification: How to Calculate

in eyepiece | Eyepiece magnification | x | 10 | 0
in objective | Objective magnification | x | 40 | 0
out total | Total magnification | x | eyepiece * objective | 0