✖️ 竖式乘法计算器（列竖式）Long Multiplication Calculator
用竖式（列竖式）计算两个整数或小数相乘，逐行显示每一位的部分积和最终结果，支持任意长度的大数，适合学生检查作业步骤。Multiply two whole numbers or decimals by long multiplication, showing each partial product row and the final answer, with no limit on length — handy for checking homework steps.
使用说明与常见问题How-to & FAQ
「竖式乘法计算器（列竖式）」是什么？What is the Long Multiplication Calculator tool?
用竖式（列竖式）计算两个整数或小数相乘，逐行显示每一位的部分积和最终结果，支持任意长度的大数，适合学生检查作业步骤。Multiply two whole numbers or decimals by long multiplication, showing each partial product row and the final answer, with no limit on length — handy for checking homework steps.
如何使用「竖式乘法计算器（列竖式）」？How do I use the Long Multiplication Calculator tool?
在「竖式乘法计算器（列竖式）」中，填写「被乘数」、「乘数」等参数，结果会随输入实时计算并显示在下方。In the Long Multiplication Calculator: Fill in "Multiplicand", "Multiplier"; results are recalculated instantly as you type.
竖式乘法怎么做？How does long multiplication work?
用被乘数分别乘以乘数的每一位，得到部分积，每往左一位就多错开一位（相当于乘以 10），最后把所有部分积相加。Multiply the top number by each digit of the bottom number to get partial products, shifting one place left for each digit (×10), then add them up.
小数怎么处理？What about decimals?
先忽略小数点按整数相乘，结果的小数位数等于两个因数小数位数之和。Ignore the decimal points and multiply as whole numbers; the answer has as many decimal places as both factors combined.
支持多大的数？How big can the numbers be?
使用 BigInt 精确计算，两个数合计最多 4,000 位，结果没有舍入误差。It uses exact BigInt arithmetic for up to 4,000 digits combined, with no rounding error.
计算精度如何？How precise are the results?
「竖式乘法计算器（列竖式）」使用 JavaScript 双精度浮点数（约 15–16 位有效数字），部分功能使用 BigInt 处理大整数。The Long Multiplication Calculator uses double-precision floating point (about 15–16 significant digits); some features use BigInt for large integers.
「竖式乘法计算器（列竖式）」免费吗？需要注册吗？Is the Long Multiplication Calculator free? Do I need an account?
「竖式乘法计算器（列竖式）」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Long Multiplication Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.