Microscope basics
Microscope magnification calculator
Two calculators: total magnification from the objective and eyepiece, and the magnification triangle (image size = actual size × magnification) for working out how big a cell really is from a drawing or a photo. Units are converted for you, which is where most mistakes happen.
Total magnification
A compound microscope magnifies twice: the objective forms a magnified image and the eyepiece magnifies that again. Multiply the two numbers engraved on them.
| Objective | × 10× eyepiece | Typical use |
|---|---|---|
| 4× (scanning) | 40× | Finding the specimen |
| 10× (low power) | 100× | Tissue layout, counting chambers |
| 40× (high power) | 400× | Individual cells |
| 100× (oil immersion) | 1000× | Bacteria, nuclear detail |
A camera is different: there is no eyepiece. What matters for a digital image is the pixel size at the sample, which depends on the objective, the camera adapter and the camera's pixels. Use the pixel size calculator for that.
Image size, actual size and magnification
image size = actual size × magnification · actual size = image size ÷ magnification · magnification = image size ÷ actual size
Worked example: a drawing of a cell measures 50 mm and the magnification is ×400. Convert first: 50 mm = 50,000 µm. Actual size = 50,000 ÷ 400 = 125 µm.
Units: 1 cm = 10 mm, 1 mm = 1000 µm, 1 µm = 1000 nm. Cells are usually given in µm (a red blood cell is about 7–8 µm across), organelles and viruses in nm.
If the image has a scale bar instead of a magnification, measure the object and the bar with a ruler: actual size = object length ÷ bar length × the bar's value. The scale bar page does that calculation too.
Questions
How do you calculate total magnification?
Multiply the objective magnification by the eyepiece magnification: a 40× objective with a 10× eyepiece gives 400×. If the microscope has an intermediate lens (an optovar or zoom), multiply by that as well.
How do you calculate actual size from magnification?
Actual size = image size ÷ magnification. Put the image size in the unit you want the answer in first: a 50 mm drawing at ×400 is 50,000 µm ÷ 400 = 125 µm.
What is the formula triangle for magnification?
Image = Actual × Magnification. Cover the one you want: Actual = Image ÷ Magnification, Magnification = Image ÷ Actual.
Does magnification change resolution?
No. Resolution depends on the numerical aperture and the wavelength, not on magnification. Magnifying beyond what the objective resolves (empty magnification) shows a bigger blur, not more detail.
Is this calculator free?
Yes. It runs in your browser and sends nothing anywhere. SlideScope, the desktop microscopy app made by the same team, is a paid app with a free preview.
Sources
Results are theoretical or arithmetic; check them against your instrument's documentation before relying on them for clinical or regulated work.
Measure on your real images
SlideScope opens 34 microscope and slide-scanner formats, CZI, ND2, SVS and LIF among them, with their own calibration, so lengths, areas, cell counts and scale bars come out in µm without setting anything up. Open a few of your own images with the free preview. Already decided? Subscribe now.