Diopter Calculator

Diopter Calculator for lens power and focal length in either direction. It also reads a glasses Rx, estimates myopia from blur and converts corneal radius and close-up lenses to D.

How the Diopter Calculator Works

The Diopter Calculator has six modes in its Calculate menu. Focal Length to Diopters is the default, and Diopters to Focal Length works the other way. Both also place an object in front of the lens and find where its image forms.

Glasses Prescription reads the sphere and cylinder from an eye prescription. Blur Distance to Diopters estimates nearsightedness from the distance where text starts to blur. Corneal Radius converts keratometer readings in millimeters into diopters.

Close-Up Camera Diopter covers the screw-on close-up lenses used in photography and filmmaking. It takes the diopter strength and the camera lens’s minimum focus distance, then gives the new focus range.

Reading the Results

The default lens has a 50 cm focal length. The Diopter Calculator returns +2.00 D, because 1 ÷ 0.500 m = 2. The first card repeats that focal length as 500 mm and 19.69 inches.

The second card places an object 60 cm from the lens. The image forms 300 cm behind it, real and upside down, at a magnification of −5.00×. This is the thin-lens rule 1 ÷ v = P − 1 ÷ u, with all distances in meters.

The third card shows what the same power would be as a contact lens, +2.05 D for glasses worn 12 mm from the eye. The fourth card reads the lens as a magnifier, 1.50× for this +2.00 D lens.

That card also lists the relaxed-eye figure, 0.50×, and the nearest 0.25 D step that glasses lenses are made in. A minus lens shows as making things smaller, since only plus lenses magnify.

Diopter Formula

A diopter is the unit of optical power. It equals one divided by the focal length in meters, so it measures how strongly a lens bends light. Plus lenses bring light to a focus, and minus lenses spread it out.

$$P = \frac{1}{f}$$

Here P is the power in diopters (D) and f is the focal length in meters. The same rule run backward gives the focal length from the power, f = 1 ÷ P.

So 1 diopter is not equal to 1 meter. The two are reciprocals, and 1 D simply means a focal length of 1 m. A 2 D lens focuses at 0.5 m, and a 4 D lens at 0.25 m. Stronger lenses have shorter focal lengths.

Mm to Diopter Conversion Formula

Focal lengths are often given in millimeters or centimeters. Divide 1,000 by the focal length in mm, or 100 by the focal length in cm, to get diopters directly without converting to meters first.

$$P = \frac{1000}{f_{mm}} = \frac{100}{f_{cm}}$$

This answers how many cm 1 diopter is. One diopter is a focal length of 100 cm, and 100 cm ÷ P gives the focal length for any power. A 250 mm focal length works out to 1,000 ÷ 250 = 4 D.

Diopter to Focal Length Chart

The table below lists common powers with their focal lengths. The Diopter Calculator shows a longer version of this chart, up to ±20 D, and marks the row closest to your lens.

Used in reverse, the Diopter Calculator acts as a diopter to focal length calculator. Minus lenses have the same focal length as plus lenses of equal power, but their focus is virtual.

A minus lens’s focus sits in front of the lens rather than behind it. The contact lens column comes from the vertex formula, P ÷ (1 − 0.012 P), for glasses 12 mm from the eye.

What Does a 2.00 Diopter Lens Mean?

A +2.00 D lens is a converging lens with a 50 cm focal length. In reading glasses, +2.00 is a common strength for close work. The plus sign marks a lens that adds focusing power, and +2.0 dioptre is the same thing in British spelling.

A −2.00 D lens has the same 50 cm focal length but spreads light out. It corrects mild nearsightedness, where distant objects look blurry. The number tells you the strength, and the sign tells you which way the lens works.

A 2.50 diopter lens has a focal length of 1 ÷ 2.5 = 0.40 m, or 40 cm. A 5 diopter lens focuses at 20 cm. So a 2.5 lens is stronger than a 2.0 lens, and 5 D is stronger than 3 D.

What Magnification Is 3 Diopters?

Magnifiers are often rated in both diopters and times. Two rules are in use. One adds 1 to the power divided by 4, giving 1.75× for a 3 D lens, with the image at the 25 cm near point. The other uses the power divided by 4 alone, 0.75×, for a relaxed eye.

$$M = 1 + \frac{P}{4}$$

The Diopter Calculator shows both on its fourth card for any plus lens. Its chart lists the 1 + P ÷ 4 value for each power. A +4.00 D reading lens works out to 2.00×, and a +10.00 D loupe to 3.50×.

By the same rules a 5 D magnifier is 1.25× or 2.25×. Which one is better depends on the job. A 5 D lens shows more detail but must be held at 20 cm. A 3 D lens works from 33 cm with a wider view.

How to Calculate Diopter From a Prescription

An eyeglass prescription lists sphere (SPH), cylinder (CYL) and axis. The sphere is the main power. The cylinder adds extra power in one direction to correct astigmatism. Both are already in diopters, in 0.25 D steps.

To boil a prescription down to one number, use the spherical equivalent. It is the sphere plus half the cylinder, and it is how to calculate the diopter of glasses with astigmatism.

The Glasses Prescription mode of the Diopter Calculator does this for you. It then reads the result against standard myopia levels and shows each meridian on its own.

$$SE = S + \frac{C}{2}$$

The default Rx is −3.50 −1.00. Its spherical equivalent is −3.50 + (−1.00 ÷ 2) = −4.00 D. The two meridians are −3.50 D and −4.50 D, and the stronger one sets the worst blur.

For a minus prescription, 100 ÷ |SE| gives the far point in centimeters. Past that distance things blur without glasses. At −4.00 D the far point is 25 cm from the glasses plane, which is why a strong myope holds a phone close.

Myopia Levels by Diopter

The International Myopia Institute sets the standard terms. In its report on defining and classifying myopia, myopia is a spherical equivalent of −0.50 D or less. High myopia is −6.00 D or less.

So −3.50 and −3.75 count as low myopia, and −8.00 is high myopia. High myopia is linked with a greater risk of retina problems later in life, which is why regular eye exams matter more at those powers.

In parts of East Asia, prescriptions are often spoken of in degrees, where 100 degrees equals 1.00 D. A range of 100 to 700 degrees means −1.00 D to −7.00 D, from mild myopia into the high range.

The Glasses Prescription mode gives this figure too. The default −4.00 D spherical equivalent reads as 400 degrees, which makes it easy to compare a prescription written either way.

From Glasses to Contacts

Contacts sit on the eye, about 12 mm closer than glasses. The third card turns the spherical equivalent into a contact lens power. For the default −4.00 D Rx that is −3.82 D, which orders as −3.75 D.

The fourth card checks the astigmatism. With 1.00 D of cylinder, a spherical lens leaves 0.50 D of blur in the worst meridian, so the card advises a toric lens. Spherical contacts are suggested only up to 0.75 D of cylinder.

At the cornea the default cylinder shrinks to about −0.91 D, and the nearest stock toric cylinder is −0.75 D. The Contact Lens Vertex Calculator works this out meridian by meridian for both eyes.

Estimating Myopia From Blur Distance

The Blur Distance mode estimates nearsightedness from a simple home test. Without glasses, cover one eye and move text slowly away until it first starts to blur. Measure from the eye to the text. This method is popular on Endmyopia, which offers a similar calculator and app.

The blur distance is your far point. A contact lens needs −1 ÷ far point in meters, so a 40 cm blur distance gives −2.50 D. Glasses sit 12 mm in front of the eye, so the glasses estimate uses the far point minus 0.012 m.

$$P_{glasses} = \frac{-1}{x – 0.012}$$

For 40 cm that gives −1 ÷ 0.388 = −2.58 D, which rounds to −2.50 D. The third card shows how sensitive the test is. A 10% shorter reading gives −2.87 D, and a 10% longer one gives −2.34 D.

Treat the result as a rough guide, not a prescription. Lighting, text contrast, focusing effort and astigmatism all move the blur point. An eye exam sets the real prescription.

Corneal Radius to Diopters

A keratometer measures the radius of curvature of the front of the cornea in millimeters. To turn that into diopters, eye-care tools use a keratometric index of 1.3375. That index folds in the weaker back surface of the cornea.

$$K = \frac{337.5}{r_{mm}}$$

The default readings are 7.80 mm and 7.60 mm. They give K1 = 43.27 D and K2 = 44.41 D, a mean K of 43.84 D, and 1.14 D of corneal astigmatism. This 337.5 rule is the standard keratometer scale.

Using the true corneal index of 1.376 gives the front surface alone. For the 7.70 mm mean radius that is 376 ÷ 7.70 = 48.83 D, about 5 D more than the keratometric value. The second card shows both.

The human eye as a whole has about 60 D of power, which means a focal length of roughly 17 mm. Most of that comes from the cornea, and the rest from the crystalline lens inside the eye.

Close-Up Diopters for Camera Lenses

The Diopter Calculator also works for a camera lens. A close-up diopter screws onto the front of the lens like a filter. It lets the lens focus closer than its minimum focus distance. Cine shooters use them on anamorphic and spherical lenses for inserts and close details.

With the camera lens set to infinity, a +3 D close-up lens focuses at 1 ÷ 3 = 33.3 cm. That far limit is measured from the diopter, which sits on the front of the lens.

Minimum focus distance is different. Lens makers measure it from the sensor plane, so the calculator first subtracts the lens length. A 60 cm minimum focus on a lens 12 cm long leaves 48 cm in front of the lens.

$$s_{near} = \frac{1}{P + \frac{1}{MFD – L}}$$

With +3 D that gives 1 ÷ (3 + 1 ÷ 0.48) = 19.67 cm. The Diopter Calculator shows the range as 19.7 to 33.3 cm, about 2.44 times closer than the lens alone. Enter 0 for lens length if your distance is already measured from the lens front.

Stacked diopters add their powers, so a +1 and a +2 act like a +3. Adding power shifts the whole range closer. The Aperture Area Calculator works from the same focal length idea for the camera lens itself.

Goggles, Binoculars and Other Lenses

As a diopter calculator for goggles, start from the Glasses Prescription mode. If your swim goggles come in sphere-only powers, use its spherical equivalent as the starting point.

Goggles sit closer to the eye than glasses do. At strong powers, the contact lens value on the third card is a better guide than the glasses value.

Binoculars have a diopter ring on one eyepiece, and riflescopes have a focusing eyepiece. Both let the eye focus sharply without glasses. The Binoculars Range Calculator handles range from a mil reticle once the image is sharp.

The eye’s 60 D of power and its pupil size also set how fine a detail it can see. The Angular Resolution Calculator works out that limit for the eye or any optical aperture.

Eyesight and Diopter Answers

These answers cover the eyesight questions people most often ask about diopters. They are general optics answers, and an eye-care professional should judge any individual prescription.

What is the normal eye diopter?

A normal eye needs no correction, so its prescription is 0.00 D, often written as plano. Small values such as −0.25 D or +0.25 D are common and often left uncorrected.

The eye’s own focusing power is a different number. The cornea and lens together give about 60 D, which focuses light onto the retina roughly 17 mm behind them.

Is 2.5 eyesight legally blind? What about minus 7?

No. Legal blindness is set by what you can see with correction, not by the prescription. The US Social Security definition is 20/200 or worse in the better eye with correcting lenses, or a visual field of 20 degrees or less.

Someone at −2.50, −7.00, −8.50 or +5.50 D who sees 20/20 with glasses is not legally blind. Strong prescriptions do need regular checks, since high myopia raises the risk of eye disease over time.

Is 2.00 bad eyesight?

A −2.00 D prescription is low myopia. Distant signs and faces blur beyond about 50 cm without glasses, but vision is normal with correction. A +2.50 D Rx is a moderate plus prescription, common for farsightedness or reading.

The lowest grade of eyeglasses is ±0.25 D, the smallest step lenses are made in. At that level the blur is mild, and an eye-care professional may or may not suggest wearing glasses full time.

Is a higher or lower diopter better?

Neither is better in itself. The diopter number only tells you how much correction a lens provides. A lower number means the eye needs less help, while a higher number means a stronger lens.

The right diopter is the one that gives clear, comfortable vision. Too much minus power can cause eyestrain, and too little leaves distant things blurred.

How do I know my diopter is correct?

The most reliable way is an eye exam, where a refraction tests lenses one step at a time. An optician can also read your current glasses with a lensmeter and compare the result with your prescription.

A home blur test can flag a large change, such as a far point that has moved much closer. Use the Diopter Calculator for that rough check, then confirm with an eye exam before buying new lenses.

Is there a diopter calculator app?

You do not need to install one. The Diopter Calculator runs in any phone or desktop browser, and inputs are processed on your own device. The Share and Print buttons save a result for later.

Dedicated apps such as the Endmyopia app measure the distance from the phone to your face with the camera. The Blur Distance mode here does the same math from a tape measure reading.