Biot-Savart Law Calculator

Estimate magnetic field strength from current and distance

This calculator is designed for a very common physics estimate: finding the magnetic field near a long, straight wire that carries a steady current. In practice, that estimate appears in lab setups, educational demonstrations, power wiring checks, sensor placement, and quick engineering sanity checks. Instead of working through constants and unit conversions each time, you can enter the current and the perpendicular distance from the wire and immediately see the field in tesla and microtesla. That makes the page useful both for a student learning how the relationship behaves and for a working reader who simply wants a reliable magnitude estimate.

The important idea is simple. A current-carrying wire produces a circular magnetic field around itself. The field gets stronger when the current increases, and it gets weaker when you move farther away. This calculator captures exactly that tradeoff. If you double the current while holding distance fixed, the field doubles. If you double the distance while holding current fixed, the field is cut in half. Those two patterns are the whole heart of the calculation, and they also give you a powerful built-in error check: if your result does not respond in those directions, the input values or units probably need another look.

What this page calculates and what it does not

The Biot-Savart law is a general law for magnetic fields produced by steady currents, but this specific page uses the well-known simplified result for an effectively long straight conductor. That distinction matters. If your geometry is a loop, a finite wire segment, a coil, a solenoid, or a complicated three-dimensional path, you need a different expression or a full numerical integration. Here, the model assumes the wire is long compared with the distance to the measurement point, so end effects are small. It also assumes the surrounding medium is close to air or vacuum, where the permeability is approximately the constant μ₀.

That means the calculator is best treated as a clean long-wire estimate, not as a universal magnetic-field solver. Used in the right setting, though, it is extremely handy. A straight bus bar, a long bench wire, or a cable run can often be approximated well with this model if you care about field magnitude at a nearby point. When the geometry fits, the formula is compact and transparent, so you can understand the answer instead of treating the calculator as a black box.

Formula and physical meaning

For a long straight wire, the magnetic flux density B at distance r from a current I is

Here, B is the magnetic field in tesla, I is the current in amperes, r is the perpendicular distance in meters, and μ₀ is the permeability of free space, approximately 4π × 10^-7 T·m/A. The form of the expression tells you almost everything you need to know intuitively. Current sits in the numerator, so more current means more field. Distance sits in the denominator, so moving away reduces the field. Because the denominator is linear in r, the drop-off is inverse with distance rather than inverse-square for this special geometry.

If you want the full Biot-Savart viewpoint, the long-wire expression comes from adding up the contributions of tiny current elements along the conductor. In differential form, the law can be written as

On a page like this, you do not need to perform that integration manually, but it is useful to know where the simplified formula comes from. Any calculator can be summarized abstractly as a result that depends on its inputs:

For magnetic-field problems, one common numerical idea is to break a conductor into small segments and sum each segment’s contribution. That is why the following summation view is still relevant to the Biot-Savart law, even though this specific calculator uses the closed-form straight-wire result:

In a more advanced numerical model, each segment of wire would play the role of one contribution in that sum. This page simply skips straight to the finished expression for the long-wire case, which is why it is fast, transparent, and easy to use.

How to choose the inputs correctly

The first input is the current I in amperes. Use the current flowing through the wire whose field you are estimating. If you only care about field strength, enter the current magnitude as a positive number. In a full vector treatment, the sign of current changes the field direction according to the right-hand rule, but the size of the field at a given distance depends on the magnitude. The current should represent a steady or slowly varying value. If the current is rapidly alternating at high frequency, then induced effects, phase relationships, and geometry details can matter more than this simple estimate captures.

The second input is the distance r in meters. This is not the length of the wire and not the distance measured along the wire. It is the shortest perpendicular distance from the wire to the point where you want the field. That distinction is one of the most common sources of wrong answers. If your point is 5 centimeters from the wire, enter 0.05 m, not 5 and not 50. Because the formula divides by r, even a modest unit mistake can change the result by a factor of ten or one hundred very quickly.

A helpful shortcut for mental checks is to remember the microtesla form of the same relationship. Since 1 tesla equals 1,000,000 microtesla, the long-wire formula becomes approximately B(µT) = 0.2I/r when I is in amperes and r is in meters. That is not a separate model; it is just the same equation expressed in more convenient everyday units. If you know that shortcut, you can estimate the order of magnitude before you even press the compute button.

Worked example

Suppose a straight wire carries 12 A and you want the magnetic field at a point 0.05 m away. Using the microtesla shortcut gives a fast estimate: B(µT) = 0.2 × 12 / 0.05 = 48 µT. Converting back to tesla gives 4.8 × 10^-5 T. When you enter 12 for current and 0.05 for distance, the calculator returns that same result. This example is useful because 48 µT is on the same order as Earth’s magnetic field in many locations, so the number feels physically meaningful rather than abstract.

Now use the same example to build intuition. If the distance increases from 0.05 m to 0.10 m while current stays at 12 A, the field falls to 24 µT. If instead the current doubles from 12 A to 24 A while distance stays at 0.05 m, the field rises to 96 µT. Those comparisons show the two scaling rules clearly. Distance changes can be just as important as current changes, which is why cable routing and sensor placement can matter so much in practical design work.

How to interpret the result

The result box reports the field in both tesla and microtesla. Tesla is the SI base unit, and it is the right unit for formal calculations. Microtesla is often easier to interpret in ordinary scenarios because many nearby magnetic-field values are small fractions of a tesla. For reference, Earth’s magnetic field is typically around 25 to 65 µT depending on location. So if your result is around 50 µT, you are looking at a field comparable in magnitude to Earth’s field. If your result is far below 1 µT, the wire’s field is relatively weak at that point. If it is hundreds or thousands of microtesla, the conductor is either carrying a substantial current, the point is very close to the wire, or both.

Remember that this page is reporting magnetic flux density at a point, not force, not heating, and not safety compliance by itself. Those questions usually need additional context such as frequency content, exposure standards, conductor dimensions, or magnetic materials nearby. The calculator is most valuable as a clean first estimate that tells you whether a scenario is tiny, moderate, or large enough to justify deeper analysis.

Scenario comparisons

If you are evaluating more than one setup, compare one variable at a time. That keeps cause and effect clear. The table below shows how current and distance shift the field for a few representative cases.

That kind of side-by-side comparison is often more valuable than a single isolated answer. It helps you decide whether moving a sensor, changing a cable path, or reducing current would make the biggest difference.

Assumptions and limitations

Like any compact calculator, this one becomes trustworthy only when its assumptions match the situation. The first major assumption is geometry. The wire should be long enough that the observation point is not strongly influenced by the wire’s ends. The second assumption is medium. The formula uses μ₀, which is appropriate for air or vacuum. If the field point is close to ferromagnetic cores, steel structures, or other materials that guide magnetic flux, the actual field pattern can differ significantly from the free-space estimate. The third assumption is current behavior. The Biot-Savart law itself is for steady currents, and this simplified page is best used for direct current or slowly varying current where a quasi-static picture is still reasonable.

There is also a mathematical boundary at very small distance. As r approaches zero, the simplified formula grows without bound, which tells you the model is not meant to be applied right on the axis of an idealized infinitely thin wire. Real conductors have finite size, current distribution across their cross-section, and sometimes insulation thickness that matters if you are trying to estimate the field extremely close to the surface. In other words, do not use this page to infer an exact on-conductor value at microscopic distance; use it for practical points in space near the wire.

Finally, remember that measurement uncertainty in the inputs carries straight through to the output. If current has a 10 percent uncertainty and distance has a 10 percent uncertainty, the field estimate will not be better than the data you put in. Because distance is in the denominator, a sloppy distance estimate can dominate the error budget. For many quick decisions, that is still acceptable. The goal is to know whether the field is roughly 1 µT, 10 µT, 100 µT, or higher so you can choose the next step intelligently.

Used that way, the calculator becomes more than a formula box. It becomes a fast reasoning tool. Enter a baseline case, test one adjustment at a time, and watch how the field responds. If the answers move in the expected direction and stay within the model’s assumptions, you can be confident that the estimate is telling you something real and useful.