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Scalar Multiplication Calculator

Multiply every entry of a matrix by a single scalar number to scale the whole matrix at once.
Each row must have the same number of entries
Scaled entries
6

Dimensions: 2 × 3 · scalar k = 2

Row 1
[ 2, 4, 6 ]
Row 2
[ 8, 10, 12 ]
Original A
2 × 3
Result kA
2 × 3
Scalar k
2
Entry (1,1)2
Entry (1,2)4
Entry (1,3)6
Entry (2,1)8
Entry (2,2)10
Entry (2,3)12
Step by step
  1. 1

    Rows (m)

    2
  2. 2

    Columns (n)

    3
  3. 3

    Scale factor k

    2
  4. 4

    Total entries scaled

    m × n = 2 × 3 = 6
Results are estimates for general information only and are not professional advice — always verify important results independently before relying on them. Read the full disclaimer.
Quick answer

How does this calculator work?

Scalar multiplication scales a matrix by multiplying every entry by a single number k, giving C[i][j] = k × A[i][j]. The result keeps the same m × n dimensions as the original. Enter the matrix as rows and a scalar k to scale all entries instantly, including negative, fractional, or zero scalars.

Formula
C[i][j] = k × A[i][j]
How this is calculated

Enter matrix A with one row per line; numbers within a row can be separated by spaces or commas. Every row must contain the same number of entries so the input forms a valid m × n matrix. The scalar k is a single number that can be positive, negative, a fraction, or zero.

Scalar multiplication scales each entry independently: the result C has the same dimensions m × n as A, and each entry is computed as C[i][j] = k × A[i][j]. Multiplying by k = 1 leaves the matrix unchanged, k = 0 produces the zero matrix, and a negative k flips the sign of every entry.

The operation is defined for any matrix size and always preserves the shape, so no dimension matching is required. Inputs that are not numbers, or rows of unequal length, are treated as invalid and no result is shown.

Frequently asked questions

They stay the same. Scalar multiplication scales each entry but never changes the number of rows or columns, so kA has the same m × n shape as A.

Yes. Any real number works as the scalar, including negatives, decimals, and zero. Multiplying by a negative number flips the sign of every entry; multiplying by zero gives the zero matrix.

Type one row per line, separating numbers with spaces or commas. For example, "1 2 3" on one line and "4 5 6" on the next defines a 2 × 3 matrix.

Also known as

scalar multiply matrix
multiply matrix by number
matrix scalar
scale matrix
scalar multiplication
scalar times matrix

APA

TG we-Calculate Editorial Team. (2026). Scalar Multiplication Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/scalar-multiplication-calculator

Chicago

TG we-Calculate Editorial Team. "Scalar Multiplication Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/scalar-multiplication-calculator.

IEEE

TG we-Calculate Editorial Team, "Scalar Multiplication Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/scalar-multiplication-calculator

BibTeX

@misc{wecalculate_scalar_multiplication_calculator, title = {Scalar Multiplication Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/scalar-multiplication-calculator}}, year = {2026}, note = {TG we-Calculate} }

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