The total magnification formula
A compound light microscope magnifies in two stages. The objective forms an enlarged intermediate image inside the tube, and the eyepiece (ocular) enlarges that image again for your eye. Because the two stages multiply, the total magnification formula is:
Total magnification = eyepiece magnification × objective magnification
Both values are engraved on the optics. Eyepieces are usually marked 10x (sometimes 15x or 20x), and each objective carries its magnification and numerical aperture, for example “40/0.65”. If you are unsure which part is which, our guide to compound light microscope parts shows where each lens sits.
How to calculate total magnification of a compound microscope: step by step
- Read the magnification engraved on the eyepiece (for example 10x).
- Check which objective is clicked into the light path on the revolving nosepiece.
- Read that objective's magnification (4x, 10x, 40x or 100x on a typical student microscope).
- Multiply the two numbers: 10 × 40 = 400x.
- If the microscope has an extra magnification changer or a tube factor marked on the body, multiply by that value too.
- Recalculate every time you switch objectives or eyepieces.
The table below shows the standard combinations with a 10x eyepiece, including the classroom terms LPO (low-power objective) and HPO (high-power objective).
| Objective | Common name | Eyepiece | Total magnification |
|---|---|---|---|
| 4x | Scanning objective | 10x | 40x |
| 10x | Low-power objective (LPO) | 10x | 100x |
| 40x | High-power objective (HPO, “high dry”) | 10x | 400x |
| 100x | Oil immersion objective | 10x | 1000x |
Worked examples
Example 1: changing the eyepiece
A 15x eyepiece with the 10x objective gives 15 × 10 = 150x. With the 40x objective the same eyepiece gives 600x.
Example 2: an intermediate magnification changer
Some research stands have a built-in changer with a 1.5x position. With a 10x eyepiece, a 40x objective and the changer at 1.5x, total magnification is 10 × 40 × 1.5 = 600x. The same logic applies to any extra lens in the light path: every factor is multiplied.
Example 3: working backwards
If a worksheet says the total magnification is 400x and the eyepiece is 10x, the objective must be 400 ÷ 10 = 40x. Dividing total magnification by one known factor always gives the missing one.
How to calculate total magnification of a stereomicroscope
Stereo (dissecting) microscopes usually have a zoom body instead of interchangeable objectives, and may use an auxiliary lens screwed under the body. The principle is the same: multiply every factor in the light path.
Total magnification = eyepiece × zoom setting × auxiliary lens
With 10x eyepieces, the zoom knob at 2.5 and a 1.5x auxiliary lens, total magnification is 10 × 2.5 × 1.5 = 37.5x. Remove the auxiliary lens and it drops to 25x. A 0.5x auxiliary lens does the opposite: it halves magnification but gives a larger field of view and a longer working distance, which is useful for bigger specimens.
Total magnification of an image or drawing
A different question appears in biology homework: how much is a drawing or a photo enlarged compared with the real specimen? Here the formula is:
Magnification = image size ÷ actual size
Use the same units for both. If a cell measures 40 mm in a printed micrograph and its real diameter is 0.1 mm (100 µm), the image magnification is 40 ÷ 0.1 = 400x. This is why scientific images carry a scale bar: the printed size of a photo changes on every screen and page, but a scale bar stays correct.
A related quick estimate is the field of view. Dividing the eyepiece field number (often 18–22 mm, engraved on the eyepiece) by the objective magnification gives the diameter of the visible circle at the specimen. A field number of 20 with a 40x objective means a field about 0.5 mm wide.
Microscope resolution vs magnification
Magnification tells you how big the image is; resolution tells you how close two points can be and still appear separate. Resolution does not depend on magnification at all. Nikon's MicroscopyU expresses it with formulas such as r = 0.61λ / NA, where λ is the wavelength of light and NA is the numerical aperture of the objective.
In practice, this means the objective sets the limit. MicroscopyU lists a resolution of about 0.29 µm for an NA 0.95 objective in green light (550 nm) and about 0.20 µm for a 100x oil-immersion plan apochromat with NA 1.40. Shorter wavelengths resolve finer detail: at NA 0.95 the figure improves to roughly 0.19 µm at 360 nm and worsens to about 0.37 µm at 700 nm. A properly adjusted condenser is also needed to reach these values.
That limit is why electron microscopes, which use electrons with far shorter wavelengths, can resolve structures that no light microscope can. See our overview of how a scanning electron microscope works.
Useful magnification and empty magnification
MicroscopyU gives a widely used rule of thumb: the useful magnification range is about 500 to 1000 times the NA of the objective. Below 500 × NA, your eye cannot pick out all the detail the objective captures. Above 1000 × NA you get empty magnification: the image grows, but no new detail appears, and blur, halos and diffraction effects become more visible.
| Objective (typical NA) | Useful range (500–1000 × NA) | With 10x eyepiece | With 20x eyepiece |
|---|---|---|---|
| 4x / 0.10 | 50x – 100x | 40x (slightly below range) | 80x (within range) |
| 10x / 0.25 | 125x – 250x | 100x (slightly below range) | 200x (within range) |
| 40x / 0.65 | 325x – 650x | 400x (within range) | 800x (empty magnification) |
| 100x / 1.25 oil | 625x – 1250x | 1000x (within range) | 2000x (empty magnification) |
The NA values above are typical for basic achromatic objectives; always read the actual value engraved on yours. MicroscopyU also notes a practical consequence: for 250x, a 10x objective with a 25x eyepiece shows more detail than a 25x objective with a 10x eyepiece, because the higher-NA objective does the resolving.
Key takeaway: total magnification is simple multiplication, but detail comes from the objective's numerical aperture. When you need to see more, switch to a higher-NA objective rather than a stronger eyepiece.
Common mistakes when calculating magnification
- Adding instead of multiplying: 10x and 40x give 400x, not 50x.
- Forgetting extra factors: magnification changers, tube factors and auxiliary lenses all multiply in.
- Confusing camera and eye: on a monitor, displayed size depends on the camera adapter, sensor and screen, so the eyepiece formula no longer applies; use a calibrated scale bar instead.
- Mixing units: when calculating image magnification, convert mm and µm to the same unit first.
- Chasing big numbers: a cheap microscope advertised at 2000x with a 1.25 NA objective is deep in empty magnification.
Conclusion
To calculate total magnification, multiply the eyepiece by the objective and by any extra lens in the light path; for stereo microscopes, include the zoom setting and auxiliary lens. Then check the objective's numerical aperture: it decides how much real detail that magnification can show, and the 500–1000 × NA range tells you when extra magnification stops being useful.