Vedic math tricks for fast multiplication

Vedic math is a collection of multiplication and calculation shortcuts derived from a set of aphorisms ("sutras"). You don't need to know the Sanskrit names to use them — you just need two or three of the most practical tricks to cut real time off multiplication problems. This guide covers the ones that actually show up in exam-style questions.

Trick 1: Multiplying numbers near a base (Nikhilam)

This works best when both numbers are close to a power of 10 — like 100, 1000 — either just above or just below it.

The idea: find how far each number is from the base, then combine the differences instead of multiplying the full numbers.

Both numbers below the base

Example: 97 × 96, base = 100.

• 97 is 3 below 100 → deviation −3
• 96 is 4 below 100 → deviation −4
• Cross-subtract: 97 − 4 = 93 (or 96 − 3 = 93, same result) → this gives the left part of the answer
• Multiply the deviations: (−3) × (−4) = 12 → this gives the right part of the answer

Both numbers above the base

Example: 103 × 104, base = 100.

• 103 is 3 above → deviation +3
• 104 is 4 above → deviation +4
• Cross-add: 103 + 4 = 107 → left part
• Multiply deviations: 3 × 4 = 12 → right part

If the "right part" has more digits than the number of zeros in the base, carry the extra digits into the left part. Example: 108 × 107, base 100 → deviations +8 and +7. Left: 108+7=115. Right: 8×7=56. Since 56 fits in two digits (matching the two zeros in 100), the answer is straightforwardly 11556.

For a deeper walkthrough of this specific case with more edge cases (carries, mixed-sign deviations), see Multiplying numbers close to 100 (base method).

Trick 2: Multiplying near a base that isn't 10, 100, or 1000

You can also use a working base like 50, 200, or 500 by treating it as a multiple of a power of 10 and adjusting. For most exam purposes, sticking to bases of 10, 100, and 1000 covers the vast majority of useful cases, so it's worth mastering those first before extending the method.

Trick 3: Vertically and crosswise (Urdhva-Tiryagbhyam)

This is a general-purpose method that works for any two numbers, not just ones near a base — useful when Nikhilam doesn't apply cleanly.

For two-digit numbers AB × CD, compute three parts:

• Left: A × C
• Middle: (A × D) + (B × C)
• Right: B × D

Then combine, carrying over where a part exceeds one digit.

Worked example: 23 × 46

• Left: 2 × 4 = 8
• Middle: (2 × 6) + (3 × 4) = 12 + 12 = 24
• Right: 3 × 6 = 18

Now combine with carries, starting from the right: Right = 18 → write 8, carry 1. Middle = 24 + 1 (carry) = 25 → write 5, carry 2. Left = 8 + 2 (carry) = 10.

Trick 4: Multiplying by 9, 99, 999 (special case of Nikhilam)

Any number times a string of 9s is just that number's Nikhilam calculation with base 10, 100, or 1000 — but it's common enough to treat as its own shortcut.

Rule for N × 9 (or 99, 999...): subtract 1 from N, then subtract that result from the base's "all 9s" form.

When to use which trick

In a timed exam, quickly scanning the two numbers tells you which shortcut applies: both close to a round base → Nikhilam. Neither close to a base → Urdhva-Tiryagbhyam. One of them is a string of 9s → the special case. If none apply cleanly, it's often faster to just do standard multiplication than to force a Vedic method onto numbers that don't fit it well.