Understand the relationship
The reasoning behind the result
The eyepiece field number describes a physical stop
D = FN / (Mo Ma)
FN is the field number, the diameter of the usable field at the intermediate image in millimetres. Mo is effective objective magnification and Ma is any additional factor before that field stop. Dividing the stop diameter by their product maps it back to the specimen plane.
The eyepiece's angular magnification is a different quantity and is not part of this division. A 10× eyepiece does not tell you its field number. The model is a circular, unvignetted geometric field; the corrected usable image can be smaller.
A measured field can be transferred under a fixed stop
Dnew Mnew = Dref Mref
Dref is an independently measured field diameter at the reference objective-to-stop factor Mref. If the same field stop remains in place, doubling that factor halves the diameter. The reference measurement absorbs the physical stop size into the product Dref Mref.
This transfer does not apply after changing the field stop, crop, camera path or other field-limiting element. A known-diameter mode avoids inventing optical information when the field has already been calibrated.
A target field determines an optical factor
Mo,target = FN / (Dtarget Ma); A = πD²/4
After converting target diameter into millimetres, the required objective factor follows by rearranging the field-number relationship. It is an arithmetic target, not a promise that an available objective will provide the desired corrected field or match the microscope.
The circular area uses the specimen-plane diameter. Area changes with the square of diameter: halving diameter quarters field area. The output also gives diameter in millimetres and micrometres so the conversion can be checked directly.
A visual span estimate uses a linear fraction
L = fD; f = 1/N
If an observed specimen span covers fraction f of the field diameter, its estimated length is fD. Equivalently, N equal end-to-end spans would cover the diameter, so each is D/N. N may be a fractional estimate, but it must be at least one for a span that fits inside the field.
Counting all objects in the circular field is not this end-to-end measurement. Neither an area fraction nor total object count can be substituted for the linear fraction. The diagram marks only the entered central span; it does not identify specimen boundaries or correct distortion.
Follow the numbers
A 20 mm field number at 40×
- With a 40× effective objective and no additional magnification, D = 20 / (40 × 1) = 0.5 mm = 500 µm.
- The circular field area is π × 500² / 4 = 196,349.540849 µm², or approximately 0.196350 mm².
- If the observed span is one quarter of the diameter, L = 0.25 × 500 = 125 µm. Four such end-to-end spans cover the diameter.
The 125 µm result is an estimate from the entered fraction; direct calibrated micrometry is needed for a measurement of the actual boundary.
Quick guide
How to use this calculator
- Choose a known field number, a measured reference field, an already calibrated diameter or a desired diameter.
- Field number is always in millimetres at the intermediate image. All specimen-plane lengths use your selected unit.
- When transferring a reference field, retain the same field stop and use the total objective-to-field-stop factor for both configurations.
- Optionally enter a linear fraction or equivalent end-to-end spans across the diameter. Read this rough size estimate separately from calibrated image measurements.
Calculation method
Calculation and interpretation
Keep the field-stop geometry, specimen-plane diameter and observed specimen fraction connected.
D = FN/(Mo Ma); Dnew = Dref Mref/Mnew; Mo,target = FN/(Dtarget Ma); A = πD²/4; L = fD = D/N.
Worked example
A 20 mm field number at 40×
The 125 µm result is an estimate from the entered fraction; direct calibrated micrometry is needed for a measurement of the actual boundary.
D = FN/(Mo Ma); Dnew = Dref Mref/Mnew; Mo,target = FN/(Dtarget Ma); A = πD²/4; L = fD = D/N.
Supported inputs
Precision and limits
Circular geometric field only
Assumes a fixed circular field stop and a matching effective magnification. Corrected field limits, vignetting, camera crops, distortion and off-axis aberrations are not modeled.
Span estimate, not specimen analysis
No segmentation, area-to-length inference, cell identity, shape assumption or biological interpretation is supplied. Positive dimension, scale and magnification inputs support 10⁻¹² through 10¹² in their selected units. Signed displacement components may be exactly zero; nonzero components must have an absolute magnitude from 10⁻¹² through 10¹². These are numerical bounds, not equipment specifications or accuracy claims.
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