频率与时间Frequency & time
所有计算都在你的浏览器里完成。 Everything is calculated in your browser.
在任意一栏输入，其余几栏立即更新（高亮的是你输入的）。频率和周期的单位可选。Type in any row; the others update at once (the highlighted one is your input). Units of f and T are selectable.
结果（自动选择合适的单位）Results (units chosen automatically)
公式与适用条件Formulas and conditions
- f = 1/T，ω = 2π·f，f[Hz] = rpm / 60。rad 视为无量纲，所以 ω 的量纲也可写作 s⁻¹；结果同时给出 Hz 和 rad/s。π 取 IEEE 双精度的 Math.PI（相对误差约 10⁻¹⁶，远小于任何显示位数）。The radian is dimensionless, so ω can also be written in s⁻¹; both Hz and rad/s are shown. π is IEEE double-precision Math.PI (relative error ~10⁻¹⁶, far below any displayed digits).
- D = τ · frep，τ = D / frep，frep = D / τ，Trep = 1/frep，关断时间 = Trep − τ。off time = Trep − τ.
- f、T、ω 必须 > 0（0 频率对应无穷大周期，不显示）；转速只处理 rpm，输入负数会报错（请取绝对值）。
- f, T and ω must be > 0 (zero frequency means an infinite period and is not shown); rpm is handled as a magnitude, negative input is rejected (use the absolute value).
- 脉冲宽度的定义：τ 用你所用的宽度定义（方波的全宽；激光脉冲常用 FWHM）。D = τ·frep 对任何固定的定义都成立，但对非方波脉冲，D 只是“等效占空比”。必须 0 < D ≤ 1，即 τ ≤ Trep，否则脉冲会重叠，工具报错。
- Definition of pulse width: τ uses whichever definition you use (full width of a square pulse; FWHM for laser pulses). D = τ·frep holds for any fixed definition, but for non-square pulses D is only an “effective duty cycle”. Must have 0 < D ≤ 1, i.e. τ ≤ Trep; otherwise pulses would overlap and the tool reports an error.
- 不涉及脉冲能量、峰值功率、平均功率；不涉及相位、频谱展宽、抖动。Pulse energy, peak/average power, phase, spectral broadening and jitter are not covered.
显示位数只是格式，结果准确度受输入精度和所用假设限制；本工具不做不确定度传递。Displayed digits are only formatting; accuracy is limited by your inputs and the assumptions used. No uncertainty propagation is done.
使用的常数Constants used
本工具不使用物理常数。π = Math.PI（IEEE 双精度，相对误差约 1.2×10⁻¹⁶，出自 ECMAScript 语言规范）；时间和频率的前缀因子是精确的十进制数。This tool uses no physical constants. π = Math.PI (IEEE double precision, relative error about 1.2×10⁻¹⁶, from the ECMAScript specification); prefix factors for time and frequency are exact decimal numbers.