📏 計量學工具

🛡️ B 類不確定度Type B Uncertainty 輸入由校準證書、手冊或經驗給出的半寬 a 與包含因子 k，按 u_B = a / k 計算 B 類標準不確定度（非統計評定）。用於無重複資料時依據先驗資訊評定不確定度分量。Type B Uncertainty - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Metrology tools. #️⃣ ±半分度值Least Count Error 分度值誤差計算器按讀數規則估算 ±半分度值引入的讀數誤差，適合游標、千分尺等器具的誤差評估與不確定度分析。Least Count Error - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Metrology tools. ↔️ 上偏差 − 下偏差Dimensional Tolerance 尺寸公差帶計算器由上偏差與下偏差求公差大小，輔助零件尺寸公差設計，適合機械製圖與公差配合校核。Dimensional Tolerance - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Metrology tools. 👥 不同操作者間差異Gauge Reproducibility 輸入多名操作者各自測量同一零件的平均值，取其均值極差除以係數 d₂* 得到再現性 σ_o。用於評估不同操作者之間的人為讀數差異，是測量系統分析的關鍵指標。Gauge Reproducibility - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Metrology tools. 📏 解析度不確定度Resolution Uncertainty 解析度不確定度計算器求數字顯示末位分辨力引入的不確定度，適合電子儀表與數顯裝置的測量不確定度評定。Resolution Uncertainty - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Metrology tools. 🥞 合成不確定度Combined Uncertainty 合成不確定度計算器將各獨立不確定度分量按平方和開方合成，適合測量系統總不確定度評定與檢測報告溯源。Combined Uncertainty - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Metrology tools. ⭕ 圓度誤差Roundness Deviation 輸入圓周上若干測點的半徑值，取最大半徑與最小半徑之差作為圓度誤差的近似（最小區域法）。用於軸類、軸承、精密迴轉件的圓度形位公差檢測。Roundness Deviation - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Metrology tools. ↗️ 擴充套件不確定度Expanded Uncertainty 輸入合成標準不確定度與包含因子k，按 U = k×u_c 計算擴充套件不確定度，用於給出測量結果的可信區間。Expanded Uncertainty - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Metrology tools. 🥞 最壞情況累積Tolerance Stackup Worst 輸入線性尺寸鏈中各組成環的公差（可正可負），取各環公差絕對值之和得到最壞情況累積公差。用於保守地評估裝配間隙或干涉，確保極端偏差下仍能裝配。Tolerance Stackup Worst - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Metrology tools. ⬜ 最高點 − 最低點Flatness Deviation 輸入平面上若干測點的高度測量值，取最高點與最低點之差作為平面度誤差的近似（最小區域法）。適用於機加工零件、大理石平臺、量具的平面度質檢與來料驗收。Flatness Deviation - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Metrology tools. 🔁 極差法 R̄/d₂Gauge Repeatability 輸入同一操作者多次重複測量同一零件所得讀數，按極差法用平均極差 R̄ 除以 d₂ 係數求得重複性標準偏差 σ_r。用於測量系統分析（MSA）中量化量具自身的隨機波動。Gauge Repeatability - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Metrology tools. ✅ 標準器 + 重複性Calibration Uncertainty 校準不確定度合成計算器，輸入標準器引出的不確定度與重複性觀測不確定度，按方和根合成得到擴充套件不確定度，用於計量校準報告，純前端。Calibration Uncertainty - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Metrology tools. ❌ 由乘積型變數的相對不確定度求合成相對不確定度Uncertainty Propagation Product 輸入變數 x1、x2 及其標準不確定度 u1、u2，求相對合成不確定度。Uncertainty Propagation Product - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Metrology tools. 🎚️ 由偏倚與標準差求偏移修正能力指數Measurement Cgk 輸入上下規格限、測量均值 x̄ 與標準差 s，按 Cgk = min(USL−x̄, x̄−LSL) / (3·s) 計算考慮偏倚的能力指數。用於衡量測量系統既準（無偏）又精（波動小）的程度。Measurement Cgk - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Metrology tools. 🎚️ 由公差帶與測量標準差求測量能力指數Measurement Cg 輸入被測特性的上規格限 USL、下規格限 LSL 與測量過程標準差 s，按 Cg = (USL − LSL) / (6·s) 計算測量能力指數。用於評估量具分辨能力是否滿足公差帶要求（一般要求 Cg …Measurement Cg - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Metrology tools. 📉 由前後兩次測得值與時間差求漂移率Drift Rate 漂移率計算器由前後兩次測得值與時間間隔求測量系統的漂移率，評估儀器穩定性，適合計量期間核查與裝置維護。Drift Rate - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Metrology tools. ➗ 由各分量不確定度與自由度求有效自由度Effective Dof Welch 輸入各不確定度分量u_i與對應自由度ν_i，按Welch-Satterthwaite公式求合成有效自由度ν_eff，用於測量不確定度評定。Effective Dof Welch - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Metrology tools. 🛡️ 由擴充套件不確定度求單側 95% 保護帶Guard Band 95 輸入校準或測量的擴充套件不確定度 U（含包含因子 k），按 GB = 1.65·U 計算 95% 置信下的單側保護帶。用於合格判定時在規範限內側預留安全餘量，降低誤判風險。Guard Band 95 - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Metrology tools. 💯 由標準不確定度與測得值求相對不確定度Relative Uncertainty 輸入標準不確定度 u 與測得值 x，按 u_rel = u / |x| 計算相對不確定度（無量綱比值）。適用於需要以百分比形式表達測量精度的場合，如報告相對擴充套件不確定度。Relative Uncertainty - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Metrology tools. ∑ 由樣本標準差與測量次數求 A 類標準不確定度Std Dev Type a 輸入樣本標準差 s 與獨立測量次數 n，按 u_A = s / √n 計算 A 類標準不確定度（統計評定法）。用於由重複觀測資料評定測量結果的不確定度分量。Std Dev Type a - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Metrology tools. 💯 由測得值與參考值求相對偏倚Bias Percent 相對偏倚計算器由測得值與參考值求相對偏倚百分比，評估測量偏差的相對水平，適合計量確認與儀器效能評價。Bias Percent - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Metrology tools. ➖ 由測得值與參考值求絕對偏倚Bias Absolute 絕對偏倚計算器由測得值與參考標準值求絕對偏倚 x−x_ref，評估測量系統偏差，適合計量校準與檢測裝置準確度分析。Bias Absolute - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Metrology tools. ⚖️ 由測量標準差與公差帶求精度公差比Precision Tolerance Ratio 輸入測量標準差 s 與零件公差帶 Tol，按 PTR = 6·s / Tol 計算精度公差比。用於評價量具精度相對於公差的佔比，PTR < 0.1 表示測量裝置足夠精細。Precision Tolerance Ratio - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Metrology tools. 💯 由測量系統誤差與公差求 %GRRGrr Percent 輸入測量系統誤差 GRR（重複性與再現性合成）和零件公差頻寬度，計算 %GRR = GRR / 公差 × 100%。用於判斷測量系統是否可接受：通常 <10% 優秀，>30% 需改進。Grr Percent - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Metrology tools. ➕ 由靈敏係數與分量標準不確定度求合成不確定度Uncertainty Propagation Sum 輸入靈敏係數 c1、c2 與各分量標準不確定度 u1、u2，求合成不確定度。Uncertainty Propagation Sum - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Metrology tools. #️⃣ 由零件變差與測量誤差求可區分類別數Ndc Number 輸入零件間變差 PV 與測量系統誤差 GRR，按 NDC = 1.41 × PV / GRR 求可區分的零件類別數。用於判斷測量系統能否分辨出不同零件：NDC ≥ 5 才算有效。Ndc Number - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Metrology tools. 📊 類不確定度Type a Uncertainty A 類標準不確定度計算器，基於對同一量的多次重複觀測，用貝塞爾公式求實驗標準差與平均值標準不確定度，用於測量不確定度評定，純前端。Type a Uncertainty - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Metrology tools. 💯 量具重複再現分析GRR Research (% GRR ) 量具重複再現分析（GRR）工具評估測量系統中量具重複性與操作再現性佔比，判斷測量系統是否可接受，適合質量工程與六西格瑪。GRR Research (% GRR ) - free online tool. Free online tool on ToolBox — 100% client-side, no data uploaded, no install. Part of the Metrology tools.