Magnetic field estimate for a long straight wire
This Biot-Savart calculator estimates the magnetic field around a long, straight current-carrying wire, which is one of the most common back-of-the-envelope cases in electromagnetism. It is useful when you need a quick answer near a bench wire, a cable run, or a bus bar and do not want to carry μ₀ and unit conversions through by hand. Enter the current and the perpendicular distance to the observation point, and the page reports the field in both tesla and microtesla.
The relationship is easy to sanity-check. More current makes a stronger field, and moving farther from the wire makes the field weaker. If you double the current while keeping distance fixed, the field doubles. If you double the distance while keeping current fixed, the field halves. Those two proportionalities are the essential behavior of the long-wire Biot-Savart result, so they also help you catch bad units or swapped inputs quickly.
What this Biot-Savart wire calculator covers
The Biot-Savart law is general, but this calculator intentionally focuses on the long straight wire case. That means it is built for a single conductor that is much longer than the observation distance, with a point located at a perpendicular offset from the wire. It is not meant for loops, coils, finite segments, solenoids, or tangled conductor paths, because those geometries require either a different closed-form expression or a numerical integration over the actual wire shape.
The assumption of air or vacuum matters too, since the formula uses μ0. In more complicated surroundings, nearby steel, magnetic cores, or tight conductor bundles can distort the field enough that the free-space estimate is no longer enough. When the geometry really is a single long wire, though, the closed form is fast, transparent, and very practical.
Biot-Savart formula and physical meaning for a long straight wire
For a long straight wire, the magnetic flux density B at distance r from a current I is
Here, B is the magnetic flux density 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 expression shows the core Biot-Savart behavior for a long wire: current strengthens the field, while distance dilutes it in a simple inverse relationship. Because the dependence is 1/r rather than 1/r², moving farther away still matters quickly, but it does not fall off as sharply as an inverse-square law.
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
This differential expression is the reason the long-wire answer is so compact. The calculator does not need a generic weighted sum or a placeholder relation; it uses the closed-form result that comes from integrating the current elements along the wire. If the conductor is finite, bent, or part of a loop, this simplified expression stops being the right answer and you should move back to the actual geometry.
For a clean straight-wire estimate, though, the closed form is exactly the point: one current value and one perpendicular distance produce the field without extra setup.
How to choose current and distance for the straight-wire Biot-Savart formula
For the straight-wire Biot-Savart formula, the first input is current I in amperes. Use the current flowing through the wire whose magnetic field you want. If your interest is only in field magnitude, a positive number is fine. If you enter a negative current, the calculator will return a signed field to reflect direction convention, but the magnitude is still governed by the same I/r relationship.
The second input is distance r in meters. This is the shortest perpendicular distance from the wire to the point of interest, not the length of the wire and not a distance measured along the conductor. That difference matters a lot because the formula divides by r. A 5 cm spacing should be entered as 0.05 m, not 5 or 50.
A useful quick check is the microtesla form of the same long-wire expression. Because the calculator uses the Biot-Savart field B = μ₀I/(2πr), you can think of it as about B(µT) = 0.2I/r when I is in amperes and r is in meters. That is not a different model; it is simply the same formula rewritten in a handier unit system.
Worked example: 12 A at 5 cm from a long straight wire
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. The number is easy to visualize because it is in the same general range as Earth’s field in many places.
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 for a long straight wire
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. So if your result is around 50 µT, you are looking at a field that is easy to compare with familiar environmental values. 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.
Biot-Savart scenario comparisons for a long straight wire
If you are comparing more than one straight-wire Biot-Savart setup, change one variable at a time so the scaling stays obvious. The table below shows how current and distance shift the field for a few representative cases.
How current and distance change the Biot-Savart field near a long straight wire
| Current I |
Distance r |
Magnetic field B |
Interpretation |
| 12 A |
0.10 m |
2.4 × 10-5 T (24 µT) |
Doubling distance from 0.05 m halves the field. |
| 12 A |
0.05 m |
4.8 × 10-5 T (48 µT) |
This is the worked example and is comparable to Earth-field magnitude. |
| 24 A |
0.05 m |
9.6 × 10-5 T (96 µT) |
Doubling current at fixed distance doubles the field. |
| 6 A |
0.20 m |
6.0 × 10-6 T (6 µT) |
Lower current and larger distance quickly reduce the field. |
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 for the long-wire Biot-Savart model
This long-wire Biot-Savart estimate is only reliable when the wire really behaves like a long straight conductor and the observation point is not near an end. 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.