Kelvin Functions Calculator
Free online kelvin functions calculator. Enter your values and get instant results with the formula, step-by-step working, a worked example and FAQs — everything runs locally in your browser on Calcton, no signup required.
中文版：Kelvin 函数在线计算器
Kelvin 函数是贝塞尔函数的「旋转镜像」：ber(x) + i·bei(x) = J₀(x·e^(3πi/4))，ker(x) + i·kei(x) = K₀(x·e^(πi/4))。复平面转角 135° 与 45° 让原本振荡的 J₀ 变成实虚两条光滑曲线，恰好匹配交流电在圆柱导体内「趋肤效应」下的电流分布——ber/bei 之名正来自 Bessel real/imaginary 与开尔文勋爵的电缆穿透深度问题。
工程里它们叫 Kelvin 函数或 Thomson 函数：高频同轴电缆的串联内阻与内电感、电磁屏蔽效能、涡流制动器的设计公式中，ber、bei、ker、kei 直接出现在阻抗表达式的实部与虚部。小 x 时 ker(x) ≈ −(ln(x/2)+γ)、kei(x) ≈ −π/4，对数发散是 K₀ 支的指纹。
参考值
ber(1) = 0.984381781213087，bei(1) = 0.249566040036660
ker(1) = 0.286706208728316，kei(1) = −0.494994636518720
ber(5) = −6.23008247866636，bei(5) = 0.116034381550202
kei(0.01) ≈ −π/4 + 10⁻⁴，ker(0.01) ≈ −(ln 0.005 + γ) ≈ 4.7212
How to use the Kelvin Functions Calculator
- Fill in the inputs with your own numbers — every field shows what it expects.
- The result updates instantly as you type; no "Calculate" click needed.
- Read the result card for the main figure, the step-by-step formula, and practical notes.
Frequently asked questions
Is the Kelvin Functions Calculator free?
Yes — all math calculators on Calcton are free, with no sign-up required. Your inputs are processed in your browser and never sent to a server.
Is there a Chinese version of this tool?
Yes. Use the Chinese version link above — it is the same calculator with the interface in Simplified Chinese.
References
Formulas and benchmarks used by this calculator follow these published sources.
KevinContent LeadCalcton Editorial Team · Last updated 2026-09-27
Kevin maintains Calcton's formula verification and content: every calculator cites the standard it implements, worked examples are recomputed programmatically, and health benchmarks follow WHO and international guidelines.
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