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401(k) Calculator Formula

See 401(k) formulas for employee deferrals, employer match, editable limits, catch-up contributions, compounding, fees, inflation, and goals.

How do the 401(k) Calculator formulas work?

This formula page defines the variables used by the 401(k) Calculator, shows how those values are combined, and explains the order of operations behind the result. Use the worked steps to verify an estimate, compare scenarios, and understand which assumptions or rounding rules can affect the displayed answer.

Formula Overview

The calculator determines annual employee and employer deposits from salary, contribution rates, age, and editable limits. It distributes those deposits monthly, applies gross return and fees, increases salary annually, and repeats until retirement.

Separate projections calculate fee drag, lower and higher return paths, and the employee contribution percentage needed for the goal.

Variable Definitions

SymbolMeaningConvention
SySalary in year yCurrency per year
cEmployee contribution percentageDecimal rate
LageEntered age-based employee deferral limitCurrency
mEmployer match rateDecimal rate
qSalary percentage eligible for matchDecimal rate
AEntered annual-additions limitCurrency
KEntered compensation limitCurrency
BtBalance after month tCurrency
ra, faAnnual return and feeDecimal rates
wEntered withdrawal-rate assumptionDecimal rate

Employee Contribution

Seligible=min⁡(Sy,K)S_{eligible}=\min(S_y,K)
Dy=min⁡(Seligiblec,Lage)D_y=\min(S_{eligible}c,L_{age})

The contribution is the smaller of the salary-based deferral and the entered age-based employee limit.

Catch-Up Limit by Age

Lage=Lbase+{0,age<50L50,50≤age<60 or age>63L60−63,60≤age≤63L_{age}=L_{base}+\begin{cases}0,&age<50\\L_{50},&50\le age<60\ or\ age>63\\L_{60-63},&60\le age\le63\end{cases}

The additional amount applies only when catch-up modeling is enabled. The entered defaults reflect 2026 regular-plan limits, not SIMPLE 401(k) limits.

Employer Match

Mraw=mmin⁡(Dy,Seligibleq)M_{raw}=m\min(D_y,S_{eligible}q)

The engine matches only employee dollars within the entered salary cap. Actual plans may use each-paycheck formulas, true-ups, tiers, or different compensation definitions.

Annual Additions Constraint

Acap=min⁡(A,Seligible)A_{cap}=\min(A,S_{eligible})
My=max⁡(0,min⁡(Mraw,Acap−min⁡(Dy,Lbase)))M_y=\max\left(0,\min(M_{raw},A_{cap}-\min(D_y,L_{base}))\right)

The regular employee deferral and employer match are constrained by the entered annual-additions and compensation limits. Catch-up treatment is excluded from the regular employee amount in this constraint.

Annual Salary Growth

Sy+1=Sy(1+g)S_{y+1}=S_y(1+g)

Salary changes once after each modeled year. Contributions and matching are recalculated from the updated salary.

Effective Annual Return and Fee to Monthly Rates

rm=(1+ra)1/12−1r_m=(1+r_a)^{1/12}-1
fm=1−(1−fa)1/12f_m=1-(1-f_a)^{1/12}

Monthly Balance Recurrence

Cm=Dy+My12C_m=\frac{D_y+M_y}{12}
Bt=((Bt−1+Cb)(1+rm))(1−fm)+CeB_t=((B_{t-1}+C_b)(1+r_m))(1-f_m)+C_e

Only the beginning or end contribution term is used. Employee and employer deposits are combined after their annual amounts are calculated.

Fees and Fee Drag

Fee drag=FVfee free−FVwith feesFee\ drag=FV_{fee\ free}-FV_{with\ fees}
Growth=Bn−B0−∑Dy−∑MyGrowth=B_n-B_0-\sum D_y-\sum M_y

Today's Dollars and Illustrative Monthly Income

Breal=Bn(1+π)tB_{real}=\frac{B_n}{(1+\pi)^t}
Im=Bnw12I_m=\frac{B_nw}{12}

The income output does not test longevity, taxes, market sequence, required distributions, or whether the entered withdrawal rate is sustainable.

Required Employee Contribution Percentage

min⁡csuch thatBn(c)≥Goal\min c\quad\text{such that}\quad B_n(c)\ge Goal

The engine uses 70 bisection iterations from 0% to 100%. Each trial retains the entered employer match, age-based limits, salary growth, fees, and timing.

Lower, Base, and Higher Return Scenarios

rlow=max⁡(−0.99,r−v),rhigh=min⁡(1.00,r+v)r_{low}=\max(-0.99,r-v),\qquad r_{high}=\min(1.00,r+v)

Only return changes. These paths are sensitivity comparisons rather than probabilities.

Worked Calculation

The default plan starts at age 35 with $75,000, a $100,000 salary, a 10% employee rate, and a 50% match up to 6%.

  1. First-year employee contribution is $10,000.00.
  2. First-year employer match is $3,000.00.
  3. Total employee deposits are $475,754.16.
  4. Total employer match is $142,726.25.
  5. The monthly recurrence produces $2,192,925.06.
  6. Investment growth is $1,499,444.65 and fee drag is $116,520.60.
  7. Illustrative monthly income is $7,309.75.

Assumptions and Exclusions

  • The selected year and entered legal limits remain constant throughout the projection.
  • Salary changes once per modeled year; deposits are spread evenly by month.
  • Return, fee, inflation, match formula, and contribution timing remain constant.
  • Vesting, payroll timing, true-ups, after-tax deposits, loans, withdrawals, taxes, required distributions, volatility, and sequence risk are excluded.
  • Displayed currency is rounded to cents; calculations retain full engine precision.

Formula FAQ

Why can a higher employee rate stop increasing deposits?

The employee deferral or compensation limit may already cap the amount. For a useful 401(k) Calculator formula result, enter realistic values, compare relevant scenarios, check the calculation details, and review the definitions, assumptions, and limitations before using the estimate for an important decision.

Why might the employer match differ from a statement?

Actual plans can calculate match per paycheck and apply true-up or vesting provisions not modeled here. For a useful 401(k) Calculator formula result, enter realistic values, compare relevant scenarios, check the calculation details, and review the definitions, assumptions, and limitations before using the estimate for an important decision.

Does the limit year load new limits automatically?

No. The year and every dollar limit are user-entered assumptions. For a useful 401(k) Calculator formula result, enter realistic values, compare relevant scenarios, check the calculation details, and review the definitions, assumptions, and limitations before using the estimate for an important decision.

Is the monthly retirement income a safe withdrawal recommendation?

No. It is only the entered annual percentage of the ending balance divided by 12. For a useful 401(k) Calculator formula result, enter realistic values, compare relevant scenarios, check the calculation details, and review the definitions, assumptions, and limitations before using the estimate for an important decision.

References

Use the worked 401(k) examples to reproduce the formulas.

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